Scale Separation Research Articles

Effect of Dexmedetomidine with or without Midazolam during procedural dental sedation in children: a randomized controlled clinical trial

BackgroundDental anxiety is a global problem in the realm of pediatric dentistry. The use of procedural sedation is recommended to avoid substandard or unsafe dental treatment in preschoolers. This study aimed to compare the effect sedation with Dexmedetomidine with or without Midazolam in terms of sedation level, analgesic effect and ease of treatment completion in preschool children.MethodsA triple blind randomized controlled clinical trial comprised 72 healthy uncooperative children, 4–6 years old, were randomly allocated into three groups of 24 patients each: Group I patients were sedated with nebulized 5 μg/kg Dexmedetomidine (DEX), Group II with nebulized 3 μg/kg DEX followed by nebulized 0.3 mg/kg Midazolam (MID), and Group III with nebulized 0.5 mg/kg MID. Along the session, the three regimens were assessed and compared during the sedation level (children responsiveness) using the Modified Observer’s Assessment of Alertness/Sedation Scale, the analgesic effect using the Face, Leg, Activity, Cry, Consolability scale and ease of treatment completion using a separate 5-point scale. Vital signs were recorded before and during sedation, until full recovery.ResultsA significant difference was detected regarding children responsiveness during operative procedure in favour of DEX in comparison to MID and DEX/MID groups (P = 0.045). Within the DEX group, a significant difference was recorded regarding children responsiveness at optimum sedation and during the operative procedure (P = 0.04). Although, the analgesic effects of sedative drugs showed no statistically significant difference among the study groups (P = 0.20), the ease of treatment completion was statistically higher in the DEX than MID and DEX/MID groups (P = 0.03).ConclusionDexmedetomidine provides a moderate level of sedation, that allowed better patient cooperation, and easy completion of performed dental procedures.

Blackening S-folds

We construct the universal AdS4 black hole that asymptotes to the (φ, χ)-family of type IIB S-fold backgrounds dual to the conformal manifold of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 S-fold CFT’s. We present the explicit type IIB embedding of such a universal black hole for two particular asymptotics: the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 S-fold with U(2) symmetry at (φ, χ) = (0, 0) and the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 S-fold with SO(4) symmetry at (φ, χ) = (1, 0). As a byproduct, we also present a novel two-parameter family of AdS2 × M8 supersymmetric S-fold backgrounds with M8 = ℍ2 × S5 × S1 that features a parametrically-controlled scale separation involving some of the internal directions.

More Than Just Treats? Effects of Grandparental Support for Children Growing up in Adversity.

This study examined whether grandparental support is a protective factor for children's socio-emotional development in the context of adversity. Using longitudinal data from the Millennium Cohort Study, we investigated the effects of grandparental support across development in children with and without adverse childhood experiences (ACEs). Socio-emotional development was assessed with the Strengths and Difficulties Questionnaire when children were aged 3 years (N=10,186), 5 years (N=10,412) and 7 years (N=10,551). Parent-reported grandparental childcare, coresidence and financial help were assessed and parents reported on the occurrence of five ACEs: physical and emotional abuse assessed with the Straus' Conflict Tactics Scale, parental mental illness assessed with the Kessler scale, domestic violence and parental separation. We found that children with relatively higher levels of ACEs showed more prosocial behaviour and less externalizing problems when they received grandparental care compared to non-grandparental (in)formal care, but only at age 3. By age 7, children with higher levels of ACEs receiving grandparental care showed less prosocial behaviour and more externalizing problems. In addition, grandparental financial support at age 3 was related to more externalizing problems. Post-hoc analyses showed that internalizing and externalizing behaviours at age 5 were related to an increased probability of grandparental childcare at age 7, indicating that children's socio-emotional problems trigger grandparental support. Our findings point to a protective effect of grandparental care on children's socio-emotional development at age 3. Our results highlight the importance of going beyond the nuclear family towards the impact of the wider family network when examining children's socio-emotional development. RESEARCH HIGHLIGHTS: Three-year-old children with high levels of adverse childhood experiences (ACEs) show more prosocial behaviour and less externalizing behaviour when they receive grandparental care. Grandparental care has therefore protective effects on young children's socio-emotional development in the context of family adversity. Grandparents respond to children's socio-emotional problems and family adversity by increasing financial support and involvement in care. These findings underscore the importance of going beyond the nuclear family towards the impact of the wider family network when examining children's socio-emotional development.

Dynamics of morphogen source formation in a growing tissue.

A tight regulation of morphogen production is key for morphogen gradient formation and thereby for reproducible and organised organ development. Although many genetic interactions involved in the establishment of morphogen production domains are known, the biophysical mechanisms of morphogen source formation are poorly understood. Here we addressed this by focusing on the morphogen Sonic hedgehog (Shh) in the vertebrate neural tube. Shh is produced by the adjacently located notochord and by the floor plate of the neural tube. Using a data-constrained computational screen, we identified different possible mechanisms by which floor plate formation can occur, only one of which is consistent with experimental data. In this mechanism, the floor plate is established rapidly in response to Shh from the notochord and the dynamics of regulatory interactions within the neural tube. In this process, uniform activators and Shh-dependent repressors are key for establishing the floor plate size. Subsequently, the floor plate becomes insensitive to Shh and increases in size due to tissue growth, leading to scaling of the floor plate with neural tube size. In turn, this results in scaling of the Shh amplitude with tissue growth. Thus, this mechanism ensures a separation of time scales in floor plate formation, so that the floor plate domain becomes growth-dependent after an initial rapid establishment phase. Our study raises the possibility that the time scale separation between specification and growth might be a common strategy for scaling the morphogen gradient amplitude in growing organs. The model that we developed provides a new opportunity for quantitative studies of morphogen source formation in growing tissues.

Sharp habitat shifts, evolutionary tipping points and rescue: Quantifying the perilous path of a specialist species towards a refugium in a changing environment

Specialist species thriving under specific environmental conditions in narrow geographic ranges are widely recognized as heavily threatened by climate deregulation. Many might rely on both their potential to adapt and to disperse towards a refugium to avoid extinction. It is thus crucial to understand the influence of environmental conditions on the unfolding process of adaptation. Here, I study the eco-evolutionary dynamics of a sexually reproducing specialist species in a two-patch quantitative genetic model with moving optima. Thanks to a separation of ecological and evolutionary time scales and the phase-line study of the selection gradient, I derive the critical environmental speed for persistence, which reflects how the existence of a refugium impacts extinction patterns and how it relates to the cost of dispersal. Moreover, the analysis provides key insights about the dynamics that arise on the path towards this refugium. I show that after an initial increase of population size, there exists a critical environmental speed above which the species crosses a tipping point, resulting into an abrupt habitat switch. In addition, when selection for local adaptation is strong, this habitat switch passes through an evolutionary “death valley”, leading to a phenomenon related to evolutionary rescue, which can promote extinction for lower environmental speeds than the critical one.

The secondary classification of unequilibrated chondrites

AbstractThe multiplication of decimal petrologic schemes for different or the same chondrite groups evinces a lack of unified guiding principle in the secondary classification of type 1–3 chondrites. We show that the current OC, R and CO classifications can be a posteriori unified, with only minor reclassifications, if the decimal part of the subtype is defined as the ratio m = FaI/FaII of the mean fayalite contents of type I and type II chondrules, rounded to the nearest tenth (with adaptations from Cr systematics for the lowest subtypes following the past literature). This parameter is more efficiently evaluable than the oft‐used relative standard deviation of fayalite contents and defines a general metamorphic scale from M0.0 to M1, where the suffixed number is the rounded m. Type 3 chondrites thus span the range M0.0–M0.9 (i.e. subtypes 3.0–3.9) and M1 designates type 4. Corresponding applications are then proposed for other chondrite groups (with, e.g., CV secondary classification reduced to essentially three grades from M0.0 to M0.2, that is, subtypes 3.0–3.2). Known type 1 and 2 chondrites are at M0.0 (i.e. the metamorphic grade of type 3.0 chondrites), even so‐called “CY” chondrites, since our metamorphic scale is insensitive to brief heating. Independently, we define an aqueous alteration scale from A0.0 to A1.0, where the suffixed number is the (rounded) phyllosilicate fraction (PSF). For CM and CR chondrites, the alteration degrees can be characterized in terms of the thin‐section‐based criteria of previous schemes which are thus incorporated in the present framework, if in a coarser, but hereby more robust form. We propose their corresponding petrologic subtype to be 3‐PSF, rounded to the nearest tenth (so that type 1 would correspond to subtypes 2.0 and 2.1). Since nonzero alteration and metamorphic degrees remain mutually exclusive at the level of precision chosen, a single petrologic subtype ≈3+m‐PSF indeed remains a good descriptor of secondary processes for all unequilibrated chondrites, obviating the explicit mention of our separate scales unless finer subdivisions are adopted for the most primitive chondrites.

Stress-driven nonlocal homogenization method for cellular structures

Strong size-dependent mechanical behaviors can be observed in cellular structures violating the principle of scale separation and cannot be captured by classical homogenization methods. This paper proposes a stress-driven nonlocal homogenization method to capture the size-dependent mechanical behavior due to the nonlocal force of cellular structures. A nonlocal discrete element model is proposed first to describe the nonlocal deformation mechanism of cellular structures. Then, a continuum stress-driven nonlocal homogenization method is calibrated by deriving the continuum limit from the nonlocal discrete element model. The continuum homogenization method releases the assumption of scale separation by introducing an intrinsic length, which can be calibrated by high throughput numerical computation. Also, for efficient prediction of size-dependent mechanical behaviors, an offline dataset of the intrinsic length is constructed for different unit cells. With the help of the offline dataset, the proposed homogenization method improves the accuracy of the classic homogenization method and reduces the computational cost of the high-fidelity finite element method. Finally, a cellular rod under tension is used as an application to illustrate the efficiency and accuracy of the proposed homogenization method. Results indicate that compared with the classic homogenization method, the relative error of the proposed homogenization method is less than 1% which has a good consistency with the high-fidelity method. Moreover, the computational efficiency of the proposed homogenization method is more than five times that of the high-fidelity finite element method.

Evolution of Star Clusters within Galaxies Using Self-consistent Hybrid Hydro/N-body Simulations

We introduce a GPU-accelerated hybrid hydro/N-body code (Enzo-N) designed to address the challenges of concurrently simulating star clusters and their parent galaxies. This task has been exceedingly challenging, primarily due to the considerable computational time required, which stems from the substantial scale difference between galaxies (∼0.1 Mpc) and star clusters (∼parsecs). Yet, this significant scale separation means that particles within star clusters perceive those outside the star cluster in a semistationary state. By leveraging this aspect, we integrate a direct N-body code (Nbody6++GPU) into a cosmological (magneto)hydrodynamic code (Enzo) through utilization of the semistationary background acceleration approximation. We solve the dynamics of particles within star clusters using a direct N-body solver with regularization for few-body interactions, while evolving particles outside—dark matter, gas, and stars—using a particle-mesh gravity solver and hydrodynamic methods. We demonstrate that Enzo-N successfully simulates the coevolution of star clusters and their parent galaxies, capturing phenomena such as core collapse of the star cluster and tidal stripping due to galactic tides. This comprehensive framework opens up new possibilities for studying the evolution of star clusters within galaxies, offering insights that were previously inaccessible.

Scaling up global kinetic models of pulsar magnetospheres using a hybrid force-free-PIC numerical approach

Context. The particle-in-cell approach has proven effective in modeling neutron-star and black-hole magnetospheres from first principles, but global simulations are plagued with an unrealistically small separation between the scales where microphysics operates and the system-size scales due to limited numerical resources. A legitimate concern is whether the scale separation achieved to date is large enough for results to be safely extrapolated to realistic scales. Aims. In this work, our aim is to explore the effect of scaling up physical parameters and to check whether salient features uncovered by pure kinetic models at smaller scales are still valid, with a special emphasis on particle acceleration and high-energy radiation emitted beyond the light cylinder. Methods. To reach this objective, we developed a new hybrid numerical scheme coupling the ideal force-free and the particle-in-cell methods to optimize the numerical cost of global models. We propose a domain decomposition of the magnetosphere based on the magnetic-field topology using the flux function. The force-free model is enforced along open field lines while the particle-in-cell model is restricted to the reconnecting field line region. Results. As a proof of concept, this new hybrid model is applied to simulate a weak millisecond pulsar magnetosphere with realistic scales using high-resolution axisymmetric simulations. Magnetospheric features reported by previous kinetic models are recovered, and strong synchrotron radiation above 100MeV consistent with the Fermi-LAT gamma-ray pulsar population is successfully reproduced. Conclusions.This work further consolidates the shining-reconnecting current sheet scenario as the origin of the gamma-ray emission in pulsars, as well as firmly establishing pulsar magnetospheres as at least teraelectronvolt particle accelerators.

Impact of repetitive ELM transients on ITER divertor tungsten monoblock top surfaces

Abstract Owing to the high stored energy of ITER plasmas, the heat pulses due to uncontrolled Type I edge localized modes (ELMs) can be sufficient to melt the top surface of several poloidal rows of tungsten monoblocks in the divertor strike point regions. Coupled with the melt motion associated with tungsten in the strong tokamak magnetic fields, the resulting surface damage after even a comparatively small number of such repetitive transients may have a significant impact on long-term stationary power handling capability. The permissible numbers set important boundaries on operation and on the performance required from the plasma control system. Modelling is carried out with the recently updated MEMENTO melt dynamics code, which is tailored to tackle melt motion problems characterized by a vast spatio-temporal scale separation. The crucial role of coupling between surface deformation and shallow angle heat loading in aggravating melt damage is highlighted. As a consequence, the allowable operational space in terms of ELM-induced transient heat loads is history-dependent and once deformation has occurred, weaker heat loads, incapable of melting a pristine surface, can further extend the damage.

A scaled boundary shell formulation in isogeometric analysis for static and dynamic analysis

AbstractIn modern applications of computer‐aided design (CAD) for the analysis of shell structures, isogeometric analysis is a powerful tool that integrates both design and analysis. An exact geometry description and a straightforward computation without loss of information are advantageous, especially for shell structures such as roofs, satellite hulls, or car bodies. In addition, the scaled boundary method provides a scale separation with a semi‐analytical solution procedure to consider a three‐dimensional linear elastic constitutive law. The presented approach deals with a scaled boundary solid shell formulation in the framework of isogeometric analysis. The formulation utilizes a normal scaling strategy which scales the shell along its normal vector at each point on the discretized bottom surface. This is fundamentally different from the well‐known radial scaling strategy, where each point on the problem domain is obtained from a fixed scaling center. This results in a separation of the analysis into an in‐plane direction and a scaling (normal) direction. By introducing the scaling, a scaled boundary differential equation is derived that is dependent on the scaling parameter only. Choosing a proper set of conditions, the differential equation can be solved by a Padé expansion. While the in‐plane direction is solved in a weak sense, the thickness direction along the normal vector can be solved analytically resulting in a semi‐analytical procedure. The isogeometric description of the CAD structure inherently yields the exact normal vector, its derivatives and a higher order continuity throughout the structure. Herein, the focus is on the solution technique in the thickness direction and the challenges are addressed. The power of the formulation is outlined in several numerical examples of static and dynamic analysis and a comparison to shell formulations in literature is provided.

The mean solar butterfly diagram and poloidal field generation rate at the surface of the Sun

The difference between individual solar cycles in the magnetic butterfly diagram can mostly be ascribed to the stochasticity of the emergence process. We aim to obtain the expectation value of the butterfly diagram from observations of four cycles. This allows us to further determine the generation rate of the surface radial magnetic field. We used data from Wilcox Solar Observatory to generate time-latitude diagrams of the surface radial and toroidal magnetic fields spanning cycles 21 to 24. We symmetrized them across the equator and cycle-averaged them. From the mean butterfly diagram and surface toroidal field, we then inferred the mean poloidal field generation rate at the surface of the Sun. The averaging procedure removes realization noise from individual cycles. The amount of emerging flux required to account for the evolution of the surface radial field is found to match that provided by the observed surface toroidal field and Joy's law. Cycle-averaging butterfly diagrams removes realization noise and artefacts due to imperfect scale separation and corresponds to an ensemble average that can be interpreted in the mean-field framework. The result can then be directly compared to $ dynamo models. The Babcock-Leighton alpha -effect is consistent with observations, a result that can be appreciated only if the observational data are averaged in some way.

Safety and efficacy of a novel dexmedetomidine nasal spray for pre-anesthetic sedation in children: a randomized, double-blind, placebo-controlled trial

BackgroundOff-label intranasal administration of injectable dexmedetomidine has been widely applied in the pediatric sedation setting. However, the development of an improved drug delivery system that is easy to use is needed. We developed a novel dexmedetomidine nasal spray that can be administered directly without dilution or configuration for pediatric pre-anesthetic sedation. This nasal spray has a fixed dose and is stable during storage. To the best of our knowledge, this is the first licensed nasal spray preparation of dexmedetomidine worldwide.ObjectiveTo evaluate the pre-anesthetic sedation efficacy and safety of the novel dexmedetomidine nasal spray in children.MethodsThe study was conducted at 11 sites in China between 24 November 2021 and 20 May 2022 and was registered in ClinicalTrials.gov (NCT05111431, first registration date: 20/10/2021). Subjects (n = 159) between 2 and 6 years old who were to undergo elective surgery were randomized to the dexmedetomidine group (n = 107) or the placebo group (n = 52) in a 2:1 ratio. The dosage was 30 µg or 50 µg based on the stratified body weight. The primary outcome measure was the proportion of subjects who achieved the desired child-parent separation and Ramsay scale ≥ 3 within 45 min of administration. Safety was monitored via the assessments of adverse events, blood pressure, heart rate, respiratory rate and blood oxygen saturation.ResultsThe proportion of subjects achieving desired parental separation and Ramsay scale ≥ 3 within 45 min was significantly higher in the dexmedetomidine group (94.4%) vs the placebo group (32.0%) (P < 0.0001). As compared with placebo, dexmedetomidine treatment led to more subjects achieving Ramsay scale ≥ 3 or UMSS ≥ 2, and shorter time to reach desired parental separation, Ramsay scale ≥ 3 and UMSS ≥ 2 (all P < 0.0001). Adverse events were reported in 90.7% and 84.0% of subjects in the dexmedetomidine and placebo groups, respectively, and all the events were mild or moderate in severity.ConclusionsThis novel dexmedetomidine nasal spray presented effective pre-anesthetic sedation in children with a tolerable safety profile.

Modes of the Sakai-Sugimoto soliton

Abstract The instanton in the Sakai-Sugimoto model corresponds to the Skyrmion on the holographic boundary - which is asymptotically flat - and is fundamentally different from the flat Minkowski space Yang-Mills instanton. We use the Atiyah-Patodi-Singer index theorem and a series of transformations to show that there are 6k zeromodes - or moduli - in the limit of infinite 't Hooft coupling of the Sakai-Sugimoto model. The implications for the low-energy baryons - the Skyrmions - on the holographic boundary, is a scale separation between 2k "heavy" massive modes and 6k-9 "light" massive modes for k&gt;1; the 9 global transformations that correspond to translations, rotations and isorotations remain as zeromodes. For k=1 there are 2 "heavy" modes and 6 zeromodes due to degeneracy between rotations and isorotations.

Hydrodynamic behavior near dynamical criticality of a facilitated conservative lattice gas.

We investigate a 2d-conservative lattice gas exhibiting a dynamical active-absorbing phase transition with critical density ρ_{c}. We derive the hydrodynamic equationfor this model, showing that all critical exponents governing the large scale behavior near criticality can be obtained from two independent ones. We show that as the supercritical density approaches criticality, distinct length scales naturally appear. Remarkably, this behavior is different from the subcritical one. Numerical simulations support the critical relations and the scale separation.

Large deviations for slow–fast processes on connected complete Riemannian manifolds

We consider a class of slow–fast processes on a connected complete Riemannian manifold M. The limiting dynamics as the scale separation goes to ∞ is governed by the averaging principle. Around this limit, we prove large deviation principles with an action-integral rate function for the slow process by nonlinear semigroup methods together with Hamilton–Jacobi–Bellman (HJB) equation techniques. Our main innovation is solving the comparison principle for viscosity solutions for the HJB equation on M and the construction of a variational viscosity solution for the non-smooth Hamiltonian, which lies at the heart of deriving the action integral representation for the rate function.

Fission and fusion of heavy nuclei induced by the passage of a radiation-mediated shock in BNS mergers

ABSTRACT We compute the structure of a Newtonian, multi-ion radiation-mediated shock (RMS) for different compositions anticipated in various stellar explosions. We use a multifluid RMS model that incorporates electrostatic coupling between the different plasma constituents as well as Coulomb friction in a self-consistent manner, and approximates the effect of pair creation and the presence of free neutrons in the shock upstream on the shock structure. We find that under certain conditions a significant velocity separation is developed between different ions in the shock downstream and demonstrate that in fast enough shocks ion–ion collisions may trigger fusion and fission events at a relatively high rate. Our analysis ignores anomalous coupling through plasma microturbulence, which might reduce the velocity spread downstream below the activation energy for nuclear reactions. A rough estimate of the scale separation in RMS suggests that for shocks propagating in binary neutron star (BNS) merger ejecta, the anomalous coupling length may exceed the radiation length, allowing a considerable composition change behind the shock via inelastic collisions of $\alpha$ particles with heavy elements at shock velocities $\beta _\mathrm{ u}\gtrsim 0.25$. A sufficient abundance of free neutrons in the shock upstream, as expected during the first second after the merger, is also expected to alter the ejecta composition through neutron capture downstream. The resultant change in the composition profile may affect the properties of the early kilonova emission. The generation of microturbulence due to velocity separation can also give rise to particle acceleration that might alter the breakout signal in supernovae and other systems.

Assessment of the Dimensionality and Comparability in Legal Cynicism Measurement

Legal cynicism refers to a general contempt of people toward the law and legal authorities. Gifford and Reisig proposed a scale to measure the construct and provided evidence for its multidimensional nature. As an extension of the research on this scale, this study provides answers to two questions relevant for applied empirical research. Should empirical studies of legal cynicism treat its subdimensions as distinct yet interrelated constructs with separate scale scores, or is it adequate to consider the scale unidimensional and use an overall scale score? Are the measurement properties of legal cynicism invariant across socio-demographic characteristics relevant to criminological research? Analyses of data from two German studies (sample 1, n = 342, 54.4% male, mean age 32.7; sample 2, n = 334, 49.40% male, mean age 46.07) revealed that the scale is not sufficiently unidimensional and that the measurement properties are invariant across age, gender, and educational status.

Rigorous Holographic Bound on AdS Scale Separation.

We give an elementary proof of the following property of unitary, interacting four-dimensional N=2 superconformal field theories: At large central charge c, there exist at least sqrt[c] single-trace, scalar superconformal primary operators with dimensions Δ≲sqrt[c] (suppressing multiplicative logarithmic corrections). This follows from a stronger, more refined bound on the spectral density in terms of the asymptotic growth rate of the central charge. The proof employs known results on the structure of Coulomb branch operators. Interpreted holographically, this bounds the possible degree of scale separation in semiclassical AdS_{5} half-maximal supergravity. In particular, the bulk must contain an infinite tower of charged scalar states of energies parametrically below the large black hole threshold E_{BH}∼c. We address the extreme case of AdS_{5} pure supergravity, ruling it out as the asymptotic limit of certain sequences in theory space, though the general question remains open.

Asymptotic solution of electromagnetic heating of skin tissue with lateral heat conduction

We study the temperature evolution in the three-dimensional skin tissue exposed to an electromagnetic beam of millimeter wavelength. The skin absorption coefficient of the beam frequency determines how deep the electromagnetic energy penetrates into the skin tissue, which gives a sub-millimeter penetration depth for a 94 GHz wave. In contrast, in the lateral directions perpendicular to the depth, the beam size is usually much larger than the penetration depth. Based on this separation of length scales, we establish an asymptotic formulation in which each term has separable dependences on the depth coordinate and on the lateral coordinates. We solve it analytically to obtain a two-term asymptotic solution of the temperature distribution in the three-dimensional skin tissue. This closed-form analytical solution provides a practical and accurate way of predicting the temperature. When the beam size is moderately larger than the penetration depth (a ratio of 20), the effect of lateral heat conduction is well captured in the asymptotic solution with maximum error less than 0.0017 in the normalized temperature of magnitude well above 1.