Thermal Lattices Research Articles

Localized and delocalized topological modes of heat.

The topological physics has sparked intensive investigations into topological lattices in photonic, acoustic, and mechanical systems, powering counterintuitive effects otherwise inaccessible with usual settings. Following the success of these endeavors in classical wave dynamics, there has been a growing interest in establishing their topological counterparts in diffusion. Here, we propose an additional real-space dimension in diffusion, and the system eigenvalues are transformed from "imaginary" to "real." By judiciously tailoring the effective Hamiltonian with coupling networks, localized and delocalized topological modes are realized in heat transfer. Simulations and experiments in active thermal lattices validate the effectiveness of the proposed theoretical strategy. This approach can be applied to establish various topological lattices in diffusion systems, offering insights into engineering topologically protected edge states in dynamic diffusive scenarios.

Diffusion model-based inverse design for thermal transparency

Generative models in the field of artificial intelligence and their applications and deployment have demonstrated their great strength in the past few years. Of the vast spectrum of generative models, diffusion probabilistic models have proven to be particularly powerful and productive, transforming notions such as text-to-image and text-to-video generation from ideas into practical applications. In our previous works, we proposed a thermal metamaterial-based periodic interparticle interaction mechanism for heat management, with a specific application in thermal transparency. To address the challenging problems associated with the inverse design of thermal metamaterial structures, we employed an autoencoder-based machine learning approach and a reinforcement learning-based approach successfully. In this work, we demonstrate that our particular problems with the inverse design of thermal metamaterial-based periodic lattices for the realization of thermal transparency can also be reframed and efficiently solved by training a generative diffusion probabilistic model that can generate the design parameters corresponding to the desired response. Furthermore, we show that for a specific response, multiple sets of design parameters can be obtained by simply performing multiple inferences with the generative diffusion probabilistic model, enabling us to select the ones that can be more economical to fabricate and implement. Our work is among the first to use a diffusion model for the inverse design of thermal metamaterial-based structures and demonstrates the effectiveness of generating low-dimensional design parameters through a diffusion model.

Nonlocal thermal diffusion in one-dimensional periodic lattice

Heat conduction in micro-structured rods can be simulated with unidimensional periodic lattices. In this paper, scale effects in conduction problems, and more generally in diffusion problems, are studied from a one-dimensional thermal lattice. The thermal lattice is governed by a mixed differential-difference equation, accounting for some spatial microstructure. Exact solutions of the linear time-dependent spatial difference equation are derived for a thermal lattice under initial uniform temperature field with some temperature perturbations at the boundary. This discrete heat equation is approximated by a continuous nonlocal heat equation built by continualization of the thermal lattice equations. It is shown that such a nonlocal heat equation may be equivalently obtained from a nonlocal Fourier's law. Exact solutions of the thermal lattice problem (discrete heat equation) are compared with the ones of the local and nonlocal heat equation. An error analysis confirms the accurate calibration of the length scale of the nonlocal diffusion law with respect to the lattice spacing. The nonlocal heat equation may efficiently capture scale effect phenomena in periodic thermal lattices.

A nonlocal Fourier's law and its application to the heat conduction of one-dimensional and two-dimensional thermal lattices

Abstract This study focuses on heat conduction in unidimensional lattices also known as microstructured rods. The lattice thermal properties can be representative of concentrated thermal interface phases in one-dimensional segmented rods. The exact solution of the linear time-dependent spatial difference equation associated with the lattice problem is presented for some given initial and boundary conditions. This exact solution is compared to the quasicontinuum approximation built by continualization of the lattice equations. A rational-based asymptotic expansion of the pseudo-differential problem leads to an equivalent nonlocal-type Fourier's law. The differential nonlocal Fourier's law is analysed with respect to thermodynamic models available in the literature, such as the Guyer–Krumhansl-type equation. The length scale of the nonlocal heat law is calibrated with respect to the lattice spacing. An error analysis is conducted for quantifying the efficiency of the nonlocal model to capture the lattice evolution problem, as compared to the local model. The propagation of error with the nonlocal model is much slower than that in its local counterpart. A two-dimensional thermal lattice is also considered and approximated by a two-dimensional nonlocal heat problem. It is shown that nonlocal and continualized heat equations both approximate efficiently the two-dimensional thermal lattice response. These extended continuous heat models are shown to be good candidates for approximating the heat transfer behaviour of microstructured rods or membranes.

A sensitivity analysis of thermal lattices kinetic parameters with respect to the spectral weighting function using ultrafine BN method

Accurate calculation of kinetic parameters is of utmost importance in the safety analysis of a nuclear reactor. In the current paper, two approaches are investigated to evaluate these parameters in energy phase space. In the first approach, these parameters are derived from an energy-continuous form of the forward and adjoint transport equations and then integrals with respect to the energy variable are replaced by weighted summations over the energy groups, while in the second approach these parameters are extracted from the multi-group forward equation and its associate adjoint equation in which their multigroup constants are weighted by forward spectrum. The difference of weighting functions in these two approaches would naturally lead to different values for the kinetic parameters. This paper mainly compares the outcome of these two approaches in calculating kinetic parameters for two main types of thermal critical lattices: Mixed Oxide (MOX) and Uranium Oxide (UOX) using ultrafine BN method. The results show that calculations which are based on using the forward weighted spectrum for generating the kinetic parameters underestimate prompt neutron generation time in both thermal lattices, while effective delayed neutron fraction is overestimated in UOX thermal lattice and underestimated in MOX one.

Optimization of neutron energy-group structure in thermal lattices using ultrafine bilinear adjoint function

To solve neutron transport equation in multigroup approach, in addition to weighting function and number of energy groups, proper selection of the group boundaries have high importance for the accuracy of the calculations. In the current paper, the bilinear combination of forward and adjoint neutron spectra is used for the optimization of 69 energy group structure of WIMSD5 lattice physics code. To remedy the energy self-shielding effect, homogeneous adjoint and forward BN equations on an ultrafine energy group structure have been solved to obtain the ultrafine forward and adjoint spectra. The coarse group intervals are selected to have equal values of bilinear function in each energy interval. In order to verify the validity of the optimized structure, infinite multiplication factor and fission rate values are calculated using WIMSD5 code for two main types of thermal critical lattices: Mixed Oxide (MOX) and Uranium Oxide (UOX). A Comparison of the results with MCNP-4C code shows that the optimized 69 group structure improves the infinite multiplication factor and fission rate in the mentioned thermal lattices.

A NOVEL APPROACH TO FIND OPTIMIZED NEUTRON ENERGY GROUP STRUCTURE IN MOX THERMAL LATTICES USING SWARM INTELLIGENCE

Energy group structure has a significant effect on the results of multigroup transport calculations. It is known that UO2–PUO2 (MOX) is a recently developed fuel which consumes recycled plutonium. For such fuel which contains various resonant nuclides, the selection of energy group structure is more crucial comparing to the UO2 fuels. In this paper, in order to improve the accuracy of the integral results in MOX thermal lattices calculated by WIMSD-5B code, a swarm intelligence method is employed to optimize the energy group structure of WIMS library. In this process, the NJOY code system is used to generate the 69 group cross sections of WIMS code for the specified energy structure. In addition, the multiplication factor and spectral indices are compared against the results of continuous energy MCNP-4C code for evaluating the energy group structure. Calculations performed in four different types of H2O moderated UO2–PuO2 (MOX) lattices show that the optimized energy structure obtains more accurate results in comparison with the WIMS original structure.

Narrow Low-Frequency Spectrum and Heat Management by Thermocrystals

By transforming heat flux from particle to wave phonon transport, we introduce a new class of engineered material to control thermal conduction. We show that rationally designed nanostructured alloys can lead to a fundamental new approach for thermal management, guiding heat as photonic and phononic crystals guide light and sound, respectively. Novel applications for these materials include heat waveguides, thermal lattices, heat imaging, thermo-optics, thermal diodes, and thermal cloaking.

Validation study of SRAC2006 code system based on evaluated nuclear data libraries for TRIGA calculations by benchmarking integral parameters of TRX and BAPL lattices of thermal reactors

The goal of this study is to present the validation study of the SRAC2006 code system based on evaluated nuclear data libraries ENDF/B-VII.0 and JENDL-3.3 for neutronics analysis of TRIGA Mark-II Research Reactor at AERE, Bangladesh. This study is achieved through the analysis of integral parameters of TRX and BAPL benchmark lattices of thermal reactors. In integral measurements, the thermal reactor lattices TRX-1, TRX-2, BAPL-UO2-1, BAPL-UO2-2 and BAPL-UO2-3 are treated as standard benchmarks for validating/testing the SRAC2006 code system as well as nuclear data libraries. The integral parameters of the said lattices are calculated using the collision probability transport code PIJ of the SRAC2006 code system at room temperature 20°C based on the above libraries. The calculated integral parameters are compared to the measured values as well as the MCNP values based on the Chinese evaluated nuclear data library CENDL-3.0. It was found that in most cases, the values of integral parameters demonstrate a good agreement with the experiment and the MCNP results. In addition, the group constants in SRAC format for TRX and BAPL lattices in fast and thermal energy range respectively are compared between the above libraries and it was found that the group constants are identical with very insignificant difference. Therefore, this analysis reflects the validation study of the SRAC2006 code system based on evaluated nuclear data libraries JENDL-3.3 and ENDF/B-VII.0 and can also be essential to implement further neutronics calculations of TRIGA Mark II research reactor at AERE, Savar, Dhaka, Bangladesh.

An investigation for an optimized neutron energy-group structure in thermal lattices using Particle Swarm Optimization

This paper describes an improvement pertaining to the energy group structure of WIMS code in thermal lattices using Particle Swarm Optimization method.The 69 group WIMS cross section library for the specified energy structure is generated using NJOY data processing system. The integral parameters of thermal reactor lattices BAPL-UO2 and TRX are calculated by WIMSD5 code using the generated library. These parameters are compared against the results of continuous energy MCNP-4C code and are served for evaluating the energy group structure. Minimization of the errors in integral parameters and multiplication factor is considered as the objective function. Calculation results show that for thermal reactor lattices where the enrichment of uranium is slight, the optimized energy group structure obtains more precise results comparing with the original WIMS structure.

Bimetallic low thermal-expansion panels of Co-base and silicide-coated Nb-base alloys for high-temperature structural applications

The fabrication and high temperature performance of low thermal expansion bimetallic lattices composed of Co-base and Nb-base alloys have been investigated. A 2D sheet lattice with a coefficient of thermal expansion (CTE) lower than the constituent materials of construction was designed for thermal cycling to 1000 °C with the use of elastic–plastic finite element analyses. The low CTE lattice consisted of a continuous network of the Nb-base alloy C-103 with inserts of high CTE Co-base alloy Haynes 188. A new coating approach wherein submicron alumina particles were incorporated into (Nb, Cr, Fe) silicide coatings was employed for oxidation protection of the Nb-base alloy. Thermal gravimetric analysis results indicate that the addition of submicron alumina particles reduced the oxidative mass gain by a factor of four during thermal cycling, increasing lifetime. Bimetallic cells with net expansion of 6 × 10 −6/°C and 1 × 10 −6/°C at 1000 °C were demonstrated and their measured thermal expansion characteristics were consistent with analytical models and finite element analysis predictions.

Validation of CENDL and JEFF evaluated nuclear data files for TRIGA calculations through the analysis of integral parameters of TRX and BAPL benchmark lattices of thermal reactors

The aim of this paper is to present the validation of evaluated nuclear data files CENDL-2.2 and JEFF-3.1.1 through the analysis of the integral parameters of TRX and BAPL benchmark lattices of thermal reactors for neutronics analysis of TRIGA Mark-II Research Reactor at AERE, Bangladesh. In this process, the 69-group cross-section library for lattice code WIMS was generated using the basic evaluated nuclear data files CENDL-2.2 and JEFF-3.1.1 with the help of nuclear data processing code NJOY99.0. Integral measurements on the thermal reactor lattices TRX-1, TRX-2, BAPL-UO 2-1, BAPL-UO 2-2 and BAPL-UO 2-3 served as standard benchmarks for testing nuclear data files and have also been selected for this analysis. The integral parameters of the said lattices were calculated using the lattice transport code WIMSD-5B based on the generated 69-group cross-section library. The calculated integral parameters were compared to the measured values as well as the results of Monte Carlo Code MCNP. It was found that in most cases, the values of integral parameters show a good agreement with the experiment and MCNP results. Besides, the group constants in WIMS format for the isotopes U-235 and U-238 between two data files have been compared using WIMS library utility code WILLIE and it was found that the group constants are identical with very insignificant difference. Therefore, this analysis reflects the validation of evaluated nuclear data files CENDL-2.2 and JEFF-3.1.1 through benchmarking the integral parameters of TRX and BAPL lattices and can also be essential to implement further neutronic analysis of TRIGA Mark-II research reactor at AERE, Dhaka, Bangladesh.

Lattice of optical islets: a novel treatment modality in photomedicine

A majority of photothermal applications of laser and non-laser light sources in medicine (in particular, in dermatology) are based on the paradigm of (extended) selective photothermolysis. However, realization of this principle in its strict form may not always be possible and/or practical. Spatial (or geometric) selectivity (as opposed to wavelength and temporal selectivity) can provide an alternative approach delivering effective and safe treatment techniques. A method of creating a lattice of localized areas of light–tissue interaction (optical islets) is an example of this ‘spatially confined’ approach. The lattice of optical islets can be formed using a variety of energy sources and delivery optics, including application of lenslet arrays, phase masks and matrices of exogenous chromophores. Using a state-of-the-art theory of optical and thermal light–tissue interactions and a comprehensive computer model of skin, we have conducted a theoretical and numerical analysis of the process of formation of such a lattice in human tissue. Effects of the wavelength, beam geometry, pulsewidth and physical properties of tissues have been considered. Conditions for obtaining optical, thermal and damage islet lattices in the human skin without inducing adverse side effects (e.g. bulk damage) have been established.

Generation and Validation of the WIMS-D5 library Based on JENDL-3.2

A WIMS-D5 library based on JENDL-3.2 has been prepared and is being tested against benchmark problems. Several sensitivity calculations for stabililty confirmation of the library were carried out, such as fission spectrum dependency and the self-shielding effects of the elastic scattering cross sections and the self-shielding effects 240Pu and 242Pu capture cross sections below 4.0 eV. The results of benchmark calculations with the libraries based on JENDL-3.2, ENDF/B-VI.5, JEF-2.2, and the 1986 WIMS-D library were intercompared. The multiplication factors for the thermal lattices are slightly underpredicted by all libraries (up to 1% with ENDF/B-VI.5). The keff values with the library based on JENDL-3.2 are slightly higher than those of ENDF/B-VI.5 and JEF-2.2. The spectral indices for the lattices with JENDL-3.2 agree with the measured quantities within the uncertainties of the experiments. The calculated amounts of some isotopes such as 149Sm, 237Np, 238Pu, 242Cm and 243Cm show large differences from the measured or reference values.

The finite-temperature phase transition in lattice SU(2) Higgs theory at weak couplings

In the weak-coupling region, at β = 8 and a λ corresponding to an intermediate Higgs mass, the Higgs transition is studied on asymmetric thermal ( N σ 3×2) lattices. A two-state signal is identified, indicating a first-order transition. Multihistogram and finite-size analysis are consistent wich such a conclusion although the evidence is rather weak. The value of the Higgs condensate v( T crit ) indicates a weakly first-order transition, in qualitive accordance with partially resummed perturbation theory. On the other hand, the latent heat and the metastability temperature range σT/ T crit exceed perturbative estimates by an order of magnitude. Higgs and vector boson masses are measured on symmetric lattices near the zero-temperature phase transition. The W-mass is found to be more sensitive to the lattice size than the Higgs mass. Masses and condensates are consistent with improved tree level relations within reasonable renormalized couplings.

The electroweak phase transition: Lattice results and comparison with perturbative predictions

The SU(2)-Higgs model with one doublet is studied at intermediate Higgs mass for a semi-realistic gauge coupling β = 8. The Higgs transition is investigated on asymmetric thermal ( N σ 3 × 2) lattices. A two-state signal is identified, indicating a first order transition. This transition appears to be more strongly first order than predicted by resummed perturbation theory.

Lattice studies at zero and finite temperature in the SU(2) Higgs model at small couplings

In the weak coupling region ( β=8, λ=0.0017235 and 0.023705) the Higgs transition is determined on symmetrical (16 4) as well as thermal (16 3 × N τ ) lattices. This transition is weakly first order and becomes weaker for larger λ. Higgs and vector boson masses are obtained near to the phase transition, consistent with a mass ratio depending on λ only. The transition temperature is obtained as a function of the Higgs mass. The results are compared with perturbative relations.

Measurement of thermal diffusivity of diamond by the light-induced thermal lattice method

The thermal diffusivity coefficient of natural diamonds is measured by optical induction of thermal diffraction lattices.

Neutron Physics Investigations for Advanced Pressurized Water Reactors

The incentive of the Kernforschungszentrum Karlsruhe (KfK) advanced pressurized water reactor (APWR) investigations is the improvement of uranium utilization in a modern Federal Republic of Germany pressurized water reactor (PWR) by replacement of the core with a high converting one. The high conversion ratio is obtained by using mixed oxide (UPu)O2 in a tight light-water-moderated triangular lattice. The harder neutron spectrum leads to higher conversion ratios, to higher fissile enrichment and fissile inventories, and to worse reactivity behavior after coolant density changes. That means that core modification of the PWR shifts its neutron physics properties in the direction of fast reactor characteristics. The analysis of available calculational methods for fast and thermal reactors showed that neither the WIMS/D code, reliable for thermal reactors, nor the approved KAPROS fast reactor code can adequately predict the reactivity of an APWR in all configurations between normal and a totally voided core. A newly developed procedure, KARBUS, within the KAPROS fast reactor code system combines the advantageous features of thermal and fast reactor calculational methods. The preliminary validation for fast, epithermal, and thermal lattices, including burnup behavior, indicates that KARBUS is an adequate tool for the APWR investigations at present. Improvements in the detailed analysis of a final APWR design and of APWR neutron physics experiments in progress are briefly discussed. Parametric calculations for a simplified model indicate that current KfK proposals for homogeneous and heterogeneous APWR cores are nearly optimum concerning the competitive properties conversion ratio and void effect in a critical core poisoned by reactor control or by fission products.

Development of thermal reactor lattice physics methods

This paper describes the reactor physics methods developed for thermal reactor lattices in India. The formulation of the models introduced is based on energy-dependent integral neutron transport theory. More emphasis was put on the development of lattice cell calculational methods which indeed form the basis of physics design of nuclear reactors. The physical formulation and the cross-sections used were subjected to comprehensive validation tests through analyses of experimental information. The comparison of computed and measured parameters have amply brought out the soundness of the physical formalism and the cross-sections used in our calculational procedures.