Pith. sign in

REVIEW 2 major objections 4 minor 37 references

Effective Medium Theory for Heat Generation Using Plasmonics: A Parabolic Transmission Problem Driven by the Maxwell System

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Heat from laser-lit plasmonic nanoparticle clusters is a sum of point sources with strengths from a Volterra–Foldy-Lax system; dense arrays reduce to one effective parabolic equation driven by the homogenized Maxwell field.

desk verdict Genuine new derivation of discrete and homogenized thermo-plasmonic models, but the stated error rate in Theorem 1.1 is not justified for the stated parameter range. read the letter →

arxiv 2411.18091 v2 pith:2OHNVKOG submitted 2024-11-27 math.AP

Xinlin Cao , Arpan Mukherjee , Mourad Sini This is my paper · ORCID
classification math.AP MSC 35C1535C2035K1035K0535P25
keywords plasmonicnanoparticlesheatgenerationeffectivemediumtheoryFoldy-Laxpoint-approximationparabolictransmissionproblemMaxwellsystemhomogenizationsubwavelengthresonance
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper establishes a rigorous route from the coupled Maxwell–heat system to computable models of light-driven heat generation in clusters of plasmonic nanoparticles. When M subwavelength metal particles are illuminated near a plasmonic resonance, the paper proves the temperature field outside the cluster is, up to an error $O(M\delta^{4-h})$, a sum of heat point sources located at the particles, whose strengths solve a coupled Volterra-type heat system and a Foldy-Lax-type algebraic system for the electric field. When the particles are densely and periodically distributed, the discrete system converges to a single effective parabolic equation whose source is built from the solution of a homogenized Maxwell system with an effective permittivity. If correct, this turns engineering questions, such as what arrangement of nanoparticles produces a desired temperature profile, into a parabolic control problem plus an internal phaseless inverse problem for the Maxwell system. The proof works through layer potentials, the spectral decomposition of the magnetization operator, and the Foldy-Lax point-approximation framework.

What carries the argument

The load-bearing objects are the layer and volume potential operators for both the heat and Maxwell systems, and the spectral structure of the magnetization operator $M^{(k)}_D[f](x) = \nabla\int_D \nabla G^{(k)}(x,y)\cdot f(y)\,dy$, whose eigenpairs $(\lambda^{(3)}_n, e^{(3)}_n)$ on the space $\nabla\mathrm{Harm}$ of gradients of harmonic functions index the plasmonic resonances. The near-resonance tuning (1.1.15), which places the incident frequency $k$ and damping $\zeta$ within $O(\delta^h)$ of the resonance values, makes $|1+\eta\lambda^{(3)}_{n_0}| \sim \delta^h$, so a single dominant mode $n_0$ survives and produces the polarization matrix $P_{D_i} = \delta^{3-h}P_B$ appearing in both the discrete and effective models. For the heat part, the heat fundamental solution $\Phi^{(m)}$ and a Volterra-type Lippmann-Schwinger equation convert the transmission problem into a system for the integrated fluxes $\sigma^{(i)}$, with solvability resting on a smallness condition that makes the kernel a contraction in $H^1(0,T)$. The Fourier-Laplace transform supplies the first coercivity estimates; the rest of the proof runs in the time domain, and the passage from discrete to continuous is a discretization-and-matching of the two Lippmann-Schwinger systems rather than classical homogenization.

What would settle it

Compute the full Maxwell–heat transmission problem for one or two gold nanoparticles at resonance for several values of $\delta$, extract the integrated flux $\sigma = \int_{\partial D} \partial_\nu u$, and check that the temperature outside the cluster matches the point-source formula of Theorem 1.1 with a residual scaling like $\delta^{4-h}$; then repeat with detuning $|k - k_{n_0}|$ much larger than $\delta^h$, where the predicted hierarchy should fail to describe the computed temperature.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is a two-step reduction of the coupled Maxwell–heat transmission problem (1.1.4). First (Theorem 1.1), for a cluster $D = \cup_{i=1}^M D_i$ of $M$ small plasmonic particles with $D_i = z_i + \delta B$, the scattered temperature field outside the cluster is, up to $O(M\delta^{4-h})$, a sum of heat point sources $$u_{\mathrm{sc}}(x,t) = -\sum_{i=1}^{M}\frac{\alpha_i}{\kappa_m}\,\mathrm{Vol}(D_i)\int_0^t \$Phi^{{(m)}}$(x,t;z_i,\tau)\,\$sigma^{{(i)}}$(\tau)\,d\tau,$$ where $\Phi^{(m)}$ is the heat fundamental solution, $\alpha_i$ and $\kappa_m$ are the thermal conductivity contrast and the background diffusion constant, and the source strengths $\sigma^{(i)}$ solve the coupled Volterra system (1.1.19) driven by the electric intensities $Q_i$ that solve the Foldy-Lax system (1.1.20). Second (Theorem 1.2), when $M\gg 1$ identical particles are arranged periodically with $h=\beta$ and inter-particle spacing $d \sim \delta^{1-\beta/3}$, the discrete law converges in the sense $u - W = O(\delta^{2(3-\beta)/7})$ to the single effective parabolic equation $((\kappa_m + b\chi_\Omega)\partial_t - \Delta)W = b\chi_\Omega F$, where $F$ is built from the homogenized Maxwell field $E_f$ solving the effective system with permittivity $\varepsilon_{\mathrm{ef}} = \varepsilon_m + A_B\chi_\Omega$. The authors derive the discrete system first for arbitrary particle distributions and impose periodicity only to pass to the continuum limit, which they note is not a necessary condition.

Load-bearing premise

The asymptotic hierarchy holds only in a narrow resonance window: both the incident frequency $k$ and the damping $\zeta$ must lie within $O(\delta^h)$ of the plasmonic resonance values so that $|1+\eta\lambda^{(3)}_{n_0}| \sim \delta^h$ selects one dominant eigenmode; illumination outside this window breaks the point-source expansion and the effective equations.

Editorial extensions

If this is right

  • Predicting heat from an arbitrary cluster costs $O(M^2)$: solve the Volterra system (1.1.19) and the Foldy-Lax system (1.1.20), then sum $M$ heat point sources with error $O(M\delta^{4-h})$.
  • For dense periodic arrays, the coupled Maxwell–heat problem is replaced by one parabolic equation $((\kappa_m + b\chi_\Omega)\partial_t - \Delta)W = b\chi_\Omega F$ whose source is determined by the homogenized Maxwell field $E_f$.
  • The effective source depends only on the electric intensity $|E_f|^2$, so heating design becomes an internal, phaseless inverse problem: recover the effective permittivity $\varepsilon_{\mathrm{ef}}$ from intensity data inside the domain.
  • The continuum error rate $O(\delta^{2(3-\beta)/7})$ gives a concrete rule for how small the particles must be, relative to resonance sharpness $h$ and heat-conductivity contrast $\beta$, for the effective medium law to hold.
  • The framework reduces light-to-heat control to two subproblems: a parabolic control problem estimating the sources needed for a desired heat profile, and a phaseless inverse problem for the Maxwell system recovering the permittivity profile that generates those sources.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the discrete Foldy-Lax system is derived for arbitrary particle positions before any periodicity is imposed, the same two-step route (Volterra plus Foldy-Lax, then matched continuous equation) is likely to produce effective heat laws for random or clustered arrangements too, a direction the authors only gesture at.
  • The resonance window $|k - k_{n_0}| \sim \delta^h$ is the physically delicate part: real laser sources have finite bandwidth, so a testable consequence is that the asymptotic hierarchy should degrade once the detuning exceeds $\delta^h$, with the dominant-mode terms ceasing to control the expansion.
  • A direct numerical check of the homogenization step is to compute the discrete electric intensities $|Q_i|^2$ on a finite periodic cluster and compare them with the homogenized intensities $|E_f(z_i)|^2$; the paper's estimate (3.9.8) predicts a specific $d^{-9/7}$ decay of the squared intensity mismatch, which is measurable.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper develops an effective medium theory for heat generation by clusters of plasmonic nanoparticles, coupling the time-harmonic Maxwell system to a parabolic transmission problem for the temperature. The two central results are: (1) Theorem 1.1, which gives a point-source (Foldy-Lax) asymptotic expansion for the heat field produced by an arbitrary discrete cluster of M nanoparticles, with the effective heat sources determined by a coupled Volterra integral and algebraic system; and (2) Theorem 1.2, which passes to a continuum limit under a periodic identical-particle scaling and derives a homogenized parabolic equation whose source term is built from the solution of an effective Maxwell equation with a Drude-type effective permittivity. The proofs use layer potentials, Fourier-Laplace transforms, spectral decompositions of the magnetization operator, and discrete-to-continuum matching.

Significance. If the theorems are correct, the paper provides a rigorous mathematical bridge between the Maxwell equations, the parabolic heat equation, and effective medium descriptions for thermo-plasmonic nanoparticle systems. The approach is original in its systematic use of Foldy-Lax point approximations instead of classical homogenization, and the explicit formulas for the effective heat conductivity and permittivity are potentially valuable for control and inverse problems in photothermal therapy and thermal imaging. The paper is technically ambitious and makes heavy but appropriate use of previously established results by the same group, including C^{0,α} regularity of the effective field and a counting lemma. However, the main theorems contain internal inconsistencies in the error exponents that currently prevent the stated asymptotic expansions from being justified in the declared parameter ranges.

major comments (2)
  1. [Section 2.4.2, end of the proof of Theorem 1.1] The displayed error bounds at the end of Section 2.4.2 are err(1) ≲ Mδ^{4-h}, err(2) ≲ Mδ^{2+β-h}, and err(3) ≲ Mδ^{3+β-h}, and the text immediately concludes a total error of O(Mδ^{4-h}). This conclusion requires β ≥ 2 for err(2) and β ≥ 1 for err(3), but Theorem 1.1 imposes no lower bound on β, only h ∈ (9/5,2) together with (1.1.16) and (1.1.17). For β < 2, err(2) is asymptotically larger than the claimed error. For example, with β=1 and h=19/10, err(2) is of order Mδ^{1.1} while the claimed error is Mδ^{2.1}; the leading dipole term in the single-inclusion expansion, obtained from (2.6.7)-(2.6.9), is of order δ^{3-h}=δ^{1.1}. Hence the point-source expansion is not shown to be asymptotically smaller than its leading term in that parameter range. The theorem must either restrict β ≥ 2 or the proof must provide a sharper estimate for err(2) that is uniform in β.
  2. [Section 3.3, final step of the proof of Theorem 1.2] The final error estimate in the proof of Theorem 1.2 does not follow from the displayed bound. The text gives err(3) = O(δ^{3-β} d^{-3/2} δ^{2β-2h} d^{-9/7}). Substituting h = β and d ∼ δ^{1-β/3} (from Assumption 1, (1.2.4)) into this expression gives an error of order δ^{(3-β)/14}, not the claimed δ^{2(3-β)/7}. Even if the intended bound was the square root δ^{β-h} d^{-9/14}, the displayed estimate as written is inconsistent. This is load-bearing because it is the final step that converts the discrete-to-continuum comparison for σ^(i) − Y(z_i,·) into the homogenization rate for u − W. Moreover, since Theorem 1.2 sets h = β ∈ (9/5,2), the discrete theorem’s error bound would require β ≥ 2, which is impossible in this range; the continuum limit therefore inherits the unresolved parameter restriction from Theorem 1.1.
minor comments (4)
  1. [Theorem 1.1 statement] The phrase 'under the conditions (1.1.6) and (1.1.17)' should almost certainly read '(1.1.16) and (1.1.17)', since (1.1.6) is the scaling regime and (1.1.16) is the resonance-tuning condition.
  2. [Equation (1.1.19)] The right-hand side of the Volterra system, containing the explicit factor δ^{β-h}, appears dimensionally inconsistent with the derivation in Section 3.2.2 where ∫_{D_i}|E|^2 is of order δ^{3-2h} and γ_m/γ_{p_i} is of order δ^β, yielding a source of order δ^{3+β-h} rather than δ^{2β-h}. Please clarify the scaling of Q_i and the role of the explicit δ^{β-h} factor.
  3. [Lemma 2.5] The definition b_j := α_j/κ_m vol(B_j) δ^{3-β} is inconsistent with the coefficient α_j/κ_m vol(D_j) appearing in the Volterra system (1.1.19); since vol(D_j) = δ^3 vol(B_j) and α_j ∼ δ^{-β}, the natural coefficient is of order δ^{3-β} without an additional δ^{3-β} factor. Please check the scaling of b_j and its use in the invertibility condition.
  4. [Throughout] The manuscript contains numerous typographical and rendering errors, including a stray 'D ·' notation in (2.4.9), mislabeled error terms in (2.5.1), and garbled superscripts in the last lines of Section 3.3. A careful proofreading pass is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the effective heat and Maxwell models are derived from the posed transmission problem via potential theory, not defined or fitted as the output.

full rationale

The derivation chain is self-contained for circularity purposes. The discrete expansion in Theorem 1.1 is obtained by solving the heat transmission problem through layer and volume potentials, then estimating the boundary flux σ(i)=∫∂Di ∂νu(i) via the boundary integral system and substituting the flux asymptotics into the pointwise representation (2.10.5)-(2.10.6); no term in this chain is a fitted parameter renamed as a prediction. The Maxwell input enters only through the known Joule source and through the spectral/polarization identity derived in Section 3.2 from the resonance assumptions (1.1.15)-(1.1.16), not by fitting the heat output. Theorem 1.2's effective parabolic equation and effective Maxwell equation are matched to the discrete Foldy-Lax and Volterra systems in Sections 3.1-3.3, with εef and bχΩ given explicitly in terms of the single-particle polarization PB and thermal contrast, not calibrated to the claimed convergence rate. The paper relies on prior results by overlapping authors, notably the counting lemma from [1] and C0,α regularity of Ef from [9], but these are quoted as external mathematical facts with their own assumptions and are not the target theorem; under the stated rules they count as independent support rather than load-bearing self-citation. The paper itself flags the near-resonance window (1.1.15) as an assumption and calls (1.2.4) an expositional simplification, which further confirms that these are hypotheses, not circular inputs. Separately, the proof's rate bookkeeping in Section 3.3 appears internally inconsistent with the stated exponent 2(3-β)/7; that is a correctness concern about the error estimate, not a reduction of the claim to its own inputs, so it does not raise the circularity score.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claims rest on a small set of hand-chosen scaling exponents (h, β, λ) and on standard potential-theoretic tools imported from the literature. No new physical particles, forces, or conserved quantities are postulated; the effective permittivity and polarization matrices are derived homogenized coefficients rather than invented entities.

free parameters (3)
  • scaling exponent h = h in (9/5, 2), with ζ ~ δ^h and |1+ηλ_n0| ~ δ^h
    Chosen by hand to make the resonance gap and the a priori estimates close; the narrow window 9/5 < h < 2 is not derived from material data.
  • thermal conductivity scaling exponent β = β > 0, set β = h in Theorem 1.2
    Assumed γ_p ~ δ^{-β}; the effective heat coefficient and the final convergence rate depend on β.
  • interparticle distance exponent λ = λ ≥ 0, with constraints such as 3-3λ-h ≥ 0 and d ~ δ^{1-β/3} in Theorem 1.2
    Controls the cluster density M ~ d^{-3} and the validity of the Foldy-Lax and homogenization estimates.
assumptions (6)
  • standard math Neumann-Poincaré and Magnetization operator spectral decomposition
    Used throughout Section 1.3 and Section 3.2.1; the complete orthonormal basis (λ_n^{(3)}, e_n^{(3)}) is invoked from [13].
  • domain assumption Silver-Müller radiation condition and well-posedness of the Maxwell scattering model
    The model in (1.2) postulates a radiating scattered field and E in L^4_loc; this enters the analysis in Section 3.
  • domain assumption Drude and Lorentz permittivity models (1.3) and (1.5)
    Physical model for ε_p; the resonance frequencies k_n0 and ζ_n0 in (1.1.15) are computed from this model.
  • domain assumption Asymptotic regime ζ ~ δ^h, γ_p ~ δ^{-β}, c_p ~ 1, M ~ d^{-3}, d ~ δ^λ
    The theorems hold only in this scaling; the paper motivates it from gold and tissue values but does not derive the regime from first principles.
  • domain assumption Periodicity and identical particles in Assumption 1 for Theorem 1.2
    Needed for the homogenized model; the paper notes that periodicity can be relaxed.
  • standard math C^{0,α} and W^{1,p} regularity of E_f, cited from [9]
    Used to control discretization errors in Section 3.2.3; this is a self-cited prior result by the same group.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Effective Medium Theory for Heat Generation Using Plasmonics: A Parabolic Transmission Problem Driven by the Maxwell System." pith.science (2026). https://pith.science/paper/2OHNVKOG

@misc{pith2026241118091,
  author       = {Pith},
  title        = {Pith review of: Effective Medium Theory for Heat Generation Using Plasmonics: A Parabolic Transmission Problem Driven by the Maxwell System},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2OHNVKOG}},
  note         = {Machine review of arXiv:2411.18091}
}
read the original abstract

The excitation of plasmonic nanoparticles by incident electromagnetic waves at frequencies near their subwavelength resonances induces localized heat generation in the surrounding medium. We develop a mathematical framework to rigorously quantify this heat generation in systems of arbitrarily distributed nanoparticles. 1. For an arbitrary discrete distribution of M nanoparticles within a bounded domain, the effective heat distribution is described by a coupled system: Volterra-type integral equations for the heat conduction and a Foldy-Lax-type system governing the self consistent electric field intensities. These equations are parameterized by the particle geometries and the local electromagnetic field interactions. The effective heat generation is computed by solving these coupled systems, with the computational complexity scaling as M^2. 2. In the case M >> 1, under natural scaling regimes, the discrete system converges to a continuum model, yielding an effective parabolic equation for the heat distribution. The source term in this homogenized parabolic model is characterized by the solution of the homogenized Maxwells equations, incorporating an effective permittivity distribution derived from the Drude model under resonance conditions. Our analysis utilizes advanced tools in potential theory, asymptotic analysis and homogenization. By leveraging layer potential representations, we derive point-wise field approximations. The coupling between the Maxwell and heat equations is resolved by analyzing the spectral properties of the nanoparticles and their scaling limits. This framework reduces the problem to two mathematical challenges: a control problem for the effective parabolic system and an internal phase-less inverse problem for the Maxwell system, thus providing a unified approach to modeling heat generation in nanoparticle clusters.

Figures

Figures reproduced from arXiv: 2411.18091 by the authors.

Figure 1.1
Figure 1.1. A schematic illustration for the global distributi [PITH_FULL_IMAGE:figures/full_fig_p009_1_1.png] view at source ↗
Figure 3.1
Figure 3.1. A schematic representation of the partitioning of t [PITH_FULL_IMAGE:figures/full_fig_p056_3_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

37 extracted references · 31 canonical work pages

  1. [9]

    X. Cao, A. Ghandriche and M. Sini, From all-dieletric nanoresonators to extended quasi-static plasmonic resonators, arXiv:2312.15149

    arXiv

  2. [1]

    Ammari, D

    H. Ammari, D. P. Challa, A. P. Choudhury, and M. Sini. The point-interaction approximation for the fields generated by contrasted bubbles at arbitrary fixed frequencies. J. Differential Equations, 267(4):2104–2191, 2019

    work page 2019

  3. [2]

    Ammari, F

    H. Ammari, F. Romero, and M. Ruiz, Heat generation with plasmonic nanoparticles, Multiscale Model. Simul., 16 (2018), pp. 356--384

    work page 2018

  4. [3]

    Amrouche, N

    C. Amrouche, N. El Houda Seloula. Lp-Theory for vector potentials and Sobolev's inequalities for vector fields. Application to the Stokes equations with pressure boundary conditions. 2011. hal-00686230

    work page 2011

  5. [4]

    Ando and H

    K. Ando and H. Kang, Analysis of plasmon resonance on smooth domains using spectral properties of the Neumann-Poincar\'e operator, J. Math. Anal. Appl., 435 (2016), pp. 162-178

    work page 2016

  6. [5]

    Baffou, C

    G. Baffou, C. Girard, and R. Quidant, Heat generation in plasmonic nanostructures: Influence of morphology, Appl. Phys. Lett., 94 (2009), pp. 153109

    work page 2009

  7. [6]

    Baffou and R

    G. Baffou and R. Quidant, Thermo-plasmonics: using metallic nanostructures as nano-sources of heat. Laser Photonics Rev. 7, No. 2, 171-187 (2013)

    work page 2013

  8. [7]

    Bamberger and T

    A. Bamberger and T. H. Duong, Formulation variationnelle espace-temps pour le calcul par potentiel retarde de la diffraction dune onde acoustique (I), Math. Meth. Appl. Sci., 8 (1986), pp. 405-435

    work page 1986

Show all 37 references
  1. [8]

    X. Cao, A. Ghandriche and M. Sini, The electromagnetic waves generated by a cluster of nanoparticles with high refractive indices, Journal of the London Mathematical Society, 2023

    2023

  2. [10]

    X. Cao, A. Ghandriche and M. Sini, Effective medium theory for Van-Der-Waals heterostructures. arXiv:2404.11859

    arXiv

  3. [11]

    W. A. Challener, Heat-assisted magnetic recording by a near-field transducer with efficient optical energy transfer, Nature Photonics, 3 (2009), pp. 220-224

    2009

  4. [12]

    Friedman, Partial differential equations of parabolic type, Prentice-Hall

    A. Friedman, Partial differential equations of parabolic type, Prentice-Hall. Inc., Englewood Cliffs, N.J., 1964

    1964

  5. [13]

    M. J. Friedman, Mathematical study of the nonlinear singular integral magnetic field equation I, SIAM J. Appl. Math., 39 (1980), pp. 14-20

    1980

  6. [14]

    Ghandriche, M

    A. Ghandriche, M. Sini, Simultaneous Reconstruction of Optical and Acoustical Properties in Photo-Acoustic Imaging using plasmonics, SIAM J. Appl. Math., Vol. 83(4), 2023

    2023

  7. [15]

    Ghandriche, M

    A. Ghandriche, M. Sini, The Calderon Problem Revisited: Reconstruction With Resonant Perturbations, 2023

    2023

  8. [16]

    Giering, I

    K. Giering, I. Lamprecht, O. Minet and G. M \"u ller, Review of thermal properties of biological tissues, Proceedings of SPIE - The International Society for Optical Engineering, 1995

    1995

  9. [17]

    Kress, Linear Integral Equations 3rd ed., Springer, New York, 2014

    R. Kress, Linear Integral Equations 3rd ed., Springer, New York, 2014

    2014

  10. [18]

    P. B. Johnson and R. W. Christy, Optical constants of the noble metals, Phys. Rev. B, 6 (1972), pp. 4370–4379, https://doi.org/https://link.aps.org/doi/10.1103/PhysRevB.6.4370

    1972 doi

  11. [19]

    X. Han, K. Xu, O. Taratula, and K. Farsad, Applications of nanoparticles in biomedical imaging, Nanoscale, 11 (2019), pp. 799-819, https://doi.org/10.1039/C8NR07769J

    2019 doi

  12. [20]

    C. S. Krishnan, P. Diagradjane, Nanoparticle-mediated thermal therapy: evolving strategies for prostate cancer therapy, Int J Hyperthermia, 26 (2010), pp. 775–89

    2010

  13. [21]

    Lechleiter and P

    A. Lechleiter and P. Monk, The time-domain Lippmann–Schwinger equation and convolution quadrature, Numerical Methods for Partial Differential Equations, 31 (2015), pp. 517–540

    2015

  14. [22]

    Lubich, On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations, Numer

    Ch. Lubich, On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations, Numer. Math., 67 (1994), pp. 365-389

    1994

  15. [23]

    Lubich, R

    Ch. Lubich, R. Schneider, Time discretization of parabolic boundary integral equations. Numer. Math. 63, 455–481 (1992). https://doi.org/10.1007/BF01385870

    1992 doi

  16. [24]

    Mukherjee and M

    A. Mukherjee and M. Sini, Acoustic Cavitation using Resonating MicroBubbles. Analysis in the Time-Domain, SIAM J. Math. Anal., vol. 55, no. 5, pp. 5575–5616, 2023

    2023

  17. [25]

    Mukherjee and M

    A. Mukherjee and M. Sini, Heat Generation Using Lorentzian Nanoparticles. The Full Maxwell System, SIAM J. Appl. Math., vol. 84, no. 1, pp. 285–315, 2024

    2024

  18. [26]

    Mukherjee and M

    A. Mukherjee and M. Sini, Dispersive Effective Model in the Time-Domain for Acoustic Waves Propagating in Bubbly Media. Submitted. arXiv:2411.18091

    arXiv

  19. [27]

    Mukherjee and M

    A. Mukherjee and M. Sini, Heat Generation Using Lorentzian Nanoparticles: Estimation via Time-Domain Techniques, SIAM J. Multiscale Modeling & Simulation, 21 (2023), pp. 542–597

    2023

  20. [28]

    Prost, F

    A. Prost, F. Poisson, and E. Bossy, Photoacoustic generation by gold nanosphere: Fromlinear to nonlinear thermoelastic in the long-pulse illumination regime, Phys. Rev. B (3),92 (2015), 115450

    2015

  21. [29]

    T. Qiu, A. Rieder, F. J. Sayas, Time-domain boundary integral equation modeling of heat transmission problems. Numer. Math. 143, 223–259 (2019)

    2019

  22. [30]

    V. Ya. Raevskii, Some properties of the operators of potential theory and their application to the investigation of the basic equation of electrostatics and magnetostatics,Theoretical and Mathematical Physics, Volume 100 (1994), No. 3, pp. 1040-1045

    1994

  23. [31]

    Ritter, On the computation of Lam\'e functions, of eigenvalues and eigenfunctions of some potential operators, Z

    S. Ritter, On the computation of Lam\'e functions, of eigenvalues and eigenfunctions of some potential operators, Z. f. angew. Math. u. Mech. 78, pages 66-72, 1998

    1998

  24. [32]

    F. J. Sayas, Retarded potentials and time domain boundary integral equations. A road map, volume 50 of Springer Series in Computational Mathematics. Springer, Cham, 2016

    2016

  25. [33]

    M. Sini, H. Wang, Estimation of the heat conducted by a cluster of small cavities and characterization of the equivalent heat conduction, Multiscale Model. Simul.,17 (2019), 1214-1251

    2019

  26. [34]

    M. Sini, H. Wang and Q. Yao, Analysis of the Acoustic Waves Reflected by a Cluster of Small Holes in the Time-Domain and the Equivalent Mass Density, Multiscale Modeling & Simulation, vol. 19, no 2 (2021), pp. 1083-1114

    2021

  27. [35]

    Triki; M

    F. Triki; M. Vauthrin, Mathematical modeling of the photoacoustic effect generated by the heating of metallic nanoparticles. Quart. Appl. Math. 76 (2018), no. 4, 673-698

    2018

  28. [36]

    G. P. Zograf and et. al., All-optical nanoscale heating and thermometry with resonant dielectric nanoparticles for controllable drug release in living cells, Laser and Photonics Reviews, 14 (2020), p. 1900082, https://doi.org/10.1002/lpor.201900082

    2020 doi

  29. [37]

    G. P. Zograf, M. I. Petrov, S. V. Makarov, and Y. S. Kivshar, All-dielectric thermo- nanophotonics, Adv. Opt. Photon., 13 (2021), pp. 643-702, https://doi.org/10.1364/AOP. 426047

    2021 doi

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.