Assessment of insulating package performance by mathematical modelling

A mathematical model has been developed in the present work to describe the temperature change in a typical insulated shipping container as a function of time. The model was created by combining steady state and transient models in a 2D geometry of a typical shipping container and was subsequently validated by an ice melt test and comparison of temperature change obtained from the model and experimental measurement. An excellent agreement was obtained between the computational model developed in this work and experimental results. In addition, a parametric study was also carried out to investigate various factors in controlling the insulation performance of the packaging. It was found that the model has capability of evaluating the effect of a wide range of packaging design parameters such as thermal conductivity, surface emissivity, packaging geometry, and sounding temperatur

Focusing of timelike worldsheets in a theory of strings

An analysis of the generalised Raychaudhuri equations for string world sheets is shown to lead to the notion of focusing of timelike worldsheets in the classical Nambu-Goto theory of strings. The conditions under which such effects can occur are obtained . Explicit solutions as well as the Cauchy initial value problem are discussed. The results closely resemble their counterparts in the theory of point particles which were obtained in the context of the analysis of spacetime singularities in General Relativity many years ago.Comment: 14 pages, RevTex, no figures, extended, to appear in Phys Rev

Linear approach to the orbiting spacecraft thermal problem

We develop a linear method for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. Our method, based on perturbation theory, is compared with heuristic linearizations of the same equations. The essential feature of the linear approach is that it provides a decomposition in thermal modes, like the decomposition of mechanical vibrations in normal modes. The stationary periodic solution of the linear equations can be alternately expressed as an explicit integral or as a Fourier series. We apply our method to a minimal thermal model of a satellite with ten isothermal parts (nodes) and we compare the method with direct numerical integration of the nonlinear equations. We briefly study the computational complexity of our method for general thermal models of orbiting spacecraft and conclude that it is certainly useful for reduced models and conceptual design but it can also be more efficient than the direct integration of the equations for large models. The results of the Fourier series computations for the ten-node satellite model show that the periodic solution at the second perturbative order is sufficiently accurate.Comment: 20 pages, 11 figures, accepted in Journal of Thermophysics and Heat Transfe

Centrifugal instability over a rotating cone

In this study, we provide a mathematical description of the onset of counter-rotating circular vortices observed for a family of slender rotating cones (of half-angles 15°, 30° and 45°) in quiescent fluid. In particular, we apply appropriate scalings and apply a change of coordinates, accounting for the effects of streamline curvature. A combined large Reynolds number and large vortex wavenumber analysis is used to obtain an estimate for the asymptotic right-hand branch of neutral stability for the family of slender rotating cones. Existing experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundary-layer flow over slender rotating cones. The mode manifests as Görtler-type counter-rotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is developed and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode. Our results confirm our earlier predictions pertaining to the existence of the new Görtler mode and capture the effects of the governing centrifugal instability mechanism. Meanwhile, favourable comparisons are drawn between numerical and asymptotic neutral stability curve predictions

Nonlinear analysis of spacecraft thermal models

We study the differential equations of lumped-parameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts (nodes): an outer part that absorbs heat from the environment as radiation of various types and radiates heat as a black-body, and an inner part that just dissipates heat at a constant rate. The resulting system of two nonlinear ordinary differential equations for the satellite's temperatures is analyzed with various methods, which prove that the temperatures approach a steady state if the heat input is constant, whereas they approach a limit cycle if it varies periodically. Secondly, we generalize those methods to study a many-node thermal model of a spacecraft: this model also has a stable steady state under constant heat inputs that becomes a limit cycle if the inputs vary periodically. Finally, we propose new numerical analyses of spacecraft thermal models based on our results, to complement the analyses normally carried out with commercial software packages.Comment: 29 pages, 4 figure

Platinum(IV)-Loaded Degraded Glycol Chitosan as Efficient Platinum(IV) Drug Delivery Platform

A new class of anticancer prodrugs was designed by combining the cytotoxicity of platinum(IV) complexes and the drug carrier properties of glycol chitosan polymers: Unsymmetrically carboxylated platinum(IV) analogues of cisplatin, carboplatin and oxaliplatin, namely (OC-6-44)-acetatodiammine(3-carboxypropanoato)dichloridoplatinum(IV), (OC-6-44)-acetaodiammine(3-carboxypropanoato)(cyclobutane-1,1-dicarboxylato)platinum(IV) and (OC-6-44)-acetato(3-carboxypropanoato)(1R,2R-cyclohexane-1,2-diamine)oxalatoplatinum(IV) were synthesised and conjugated via amide bonding to degraded glycol chitosan (dGC) polymers with different chain lengths (5, 10, 18 kDa). The 15 conjugates were investigated with 1H and 195Pt NMR spectroscopy, and average amounts of platinum(IV) units per dGC polymer molecule with ICP-MS, revealing a range of 1.3–22.8 platinum(IV) units per dGC molecule. Cytotoxicity was tested with MTT assays in the cancer cell lines A549, CH1/PA-1, SW480 (human) and 4T1 (murine). IC50 values in the low micromolar to nanomolar range were obtained, and higher antiproliferative activity (up to 72 times) was detected with dGC-platinum(IV) conjugates in comparison to platinum(IV) counterparts. The highest cytotoxicity (IC50 of 0.036 ± 0.005 µM) was determined in CH1/PA-1 ovarian teratocarcinoma cells with a cisplatin(IV)–dGC conjugate, which is hence 33 times more potent than the corresponding platinum(IV) complex and twice more potent than cisplatin. Biodistribution studies of an oxaliplatin(IV)–dGC conjugate in non-tumour-bearing Balb/C mice showed an increased accumulation in the lung compared to the unloaded oxaliplatin(IV) analogue, arguing for further activity studies

Solving random boundary heat model using the finite difference method under mean square convergence

"This is the peer reviewed version of the following article: Cortés, J. C., Romero, J. V., Roselló, M. D., Sohaly, MA. Solving random boundary heat model using the finite difference method under mean square convergence. Comp and Math Methods. 2019; 1:e1026. https://doi.org/10.1002/cmm4.1026 , which has been published in final form at https://doi.org/10.1002/cmm4.1026. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] This contribution is devoted to construct numerical approximations to the solution of the one-dimensional boundary value problem for the heat model with uncertainty in the diffusion coefficient. Approximations are constructed via random numerical schemes. This approach permits discussing the effect of the random diffusion coefficient, which is assumed a random variable. We establish results about the consistency and stability of the random difference scheme using mean square convergence. Finally, an illustrative example is presented.Spanish Ministerio de Economía y Competitividad. Grant Number: MTM2017-89664-PCortés, J.; Romero, J.; Roselló, M.; Sohaly, M. (2019). Solving random boundary heat model using the finite difference method under mean square convergence. Computational and Mathematical Methods. 1(3):1-15. https://doi.org/10.1002/cmm4.1026S11513Han, X., & Kloeden, P. E. (2017). Random Ordinary Differential Equations and Their Numerical Solution. Probability Theory and Stochastic Modelling. doi:10.1007/978-981-10-6265-0Villafuerte, L., Braumann, C. A., Cortés, J.-C., & Jódar, L. (2010). Random differential operational calculus: Theory and applications. Computers & Mathematics with Applications, 59(1), 115-125. doi:10.1016/j.camwa.2009.08.061Logan, J. D. (2004). Partial Differential Equations on Bounded Domains. Undergraduate Texts in Mathematics, 121-171. doi:10.1007/978-1-4419-8879-9_4Cannon, J. R. (1964). A Cauchy problem for the heat equation. Annali di Matematica Pura ed Applicata, 66(1), 155-165. doi:10.1007/bf02412441LinPPY.On The Numerical Solution of The Heat Equation in Unbounded Domains[PhD thesis].New York NY:New York University;1993.Li, J.-R., & Greengard, L. (2007). On the numerical solution of the heat equation I: Fast solvers in free space. Journal of Computational Physics, 226(2), 1891-1901. doi:10.1016/j.jcp.2007.06.021Han, H., & Huang, Z. (2002). Exact and approximating boundary conditions for the parabolic problems on unbounded domains. Computers & Mathematics with Applications, 44(5-6), 655-666. doi:10.1016/s0898-1221(02)00180-3Han, H., & Huang, Z. (2002). A class of artificial boundary conditions for heat equation in unbounded domains. Computers & Mathematics with Applications, 43(6-7), 889-900. doi:10.1016/s0898-1221(01)00329-7Strikwerda, J. C. (2004). Finite Difference Schemes and Partial Differential Equations, Second Edition. doi:10.1137/1.9780898717938Kloeden, P. E., & Platen, E. (1992). Numerical Solution of Stochastic Differential Equations. doi:10.1007/978-3-662-12616-5Øksendal, B. (2003). Stochastic Differential Equations. Universitext. doi:10.1007/978-3-642-14394-6Holden, H., Øksendal, B., Ubøe, J., & Zhang, T. (2010). Stochastic Partial Differential Equations. doi:10.1007/978-0-387-89488-1El-Tawil, M. A., & Sohaly, M. A. (2012). Mean square convergent three points finite difference scheme for random partial differential equations. Journal of the Egyptian Mathematical Society, 20(3), 188-204. doi:10.1016/j.joems.2012.08.017Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., Roselló, M.-D., & Sohaly, M. A. (2018). Solving the random Cauchy one-dimensional advection–diffusion equation: Numerical analysis and computing. Journal of Computational and Applied Mathematics, 330, 920-936. doi:10.1016/j.cam.2017.02.001Cortés, J. C., Jódar, L., Villafuerte, L., & Villanueva, R. J. (2007). Computing mean square approximations of random diffusion models with source term. Mathematics and Computers in Simulation, 76(1-3), 44-48. doi:10.1016/j.matcom.2007.01.020Cortés, J. C., Jódar, L., & Villafuerte, L. (2009). Random linear-quadratic mathematical models: Computing explicit solutions and applications. Mathematics and Computers in Simulation, 79(7), 2076-2090. doi:10.1016/j.matcom.2008.11.008Henderson, D., & Plaschko, P. (2006). Stochastic Differential Equations in Science and Engineering. doi:10.1142/580

Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics

The atmospheric greenhouse effect, an idea that many authors trace back to the traditional works of Fourier (1824), Tyndall (1861), and Arrhenius (1896), and which is still supported in global climatology, essentially describes a fictitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law of thermodynamics such a planetary machine can never exist. Nevertheless, in almost all texts of global climatology and in a widespread secondary literature it is taken for granted that such mechanism is real and stands on a firm scientific foundation. In this paper the popular conjecture is analyzed and the underlying physical principles are clarified. By showing that (a) there are no common physical laws between the warming phenomenon in glass houses and the fictitious atmospheric greenhouse effects, (b) there are no calculations to determine an average surface temperature of a planet, (c) the frequently mentioned difference of 33 degrees Celsius is a meaningless number calculated wrongly, (d) the formulas of cavity radiation are used inappropriately, (e) the assumption of a radiative balance is unphysical, (f) thermal conductivity and friction must not be set to zero, the atmospheric greenhouse conjecture is falsified.Comment: 115 pages, 32 figures, 13 tables (some typos corrected

Quaternary Ammonium Palmitoyl Glycol Chitosan (GCPQ) Loaded with Platinum-Based Anticancer Agents—A Novel Polymer Formulation for Anticancer Therapy

Quaternary ammonium palmitoyl glycol chitosan (GCPQ) has already shown beneficial drug delivery properties and has been studied as a carrier for anticancer agents. Consequently, we synthesised cytotoxic platinum(IV) conjugates of cisplatin, carboplatin and oxaliplatin by coupling via amide bonds to five GCPQ polymers differing in their degree of palmitoylation and quaternisation. The conjugates were characterised by 1H and 195Pt NMR spectroscopy as well as inductively coupled plasma mass spectrometry (ICP-MS), the latter to determine the amount of platinum(IV) units per GCPQ polymer. Cytotoxicity was evaluated by the MTT assay in three human cancer cell lines (A549, non-small-cell lung carcinoma; CH1/PA-1, ovarian teratocarcinoma; SW480, colon adenocarcinoma). All conjugates displayed a high increase in their cytotoxic activity by factors of up to 286 times compared to their corresponding platinum(IV) complexes and mostly outperformed the respective platinum(II) counterparts by factors of up to 20 times, also taking into account the respective loading of platinum(IV) units per GCPQ polymer. Finally, a biodistribution experiment was performed with an oxaliplatin-based GCPQ conjugate in non-tumour-bearing BALB/c mice revealing an increased accumulation in lung tissue. These findings open promising opportunities for further tumouricidal activity studies especially focusing on lung tissue

Enhancing surface heat transfer by carbon nanofins: towards an alternative to nanofluids?

Background: Nanofluids are suspensions of nanoparticles and fibers which have recently attracted much attention because of their superior thermal properties. Nevertheless, it was proven that, due to modest dispersion of nanoparticles, such high expectations often remain unmet. In this article, by introducing the notion of nanofin, a possible solution is envisioned, where nanostructures with high aspect-ratio are sparsely attached to a solid surface (to avoid a significant disturbance on the fluid dynamic structures), and act as efficient thermal bridges within the boundary layer. As a result, particles are only needed in a small region of the fluid, while dispersion can be controlled in advance through design and manufacturing processes. Results: Toward the end of implementing the above idea, we focus on single carbon nanotubes to enhance heat transfer between a surface and a fluid in contact with it. First, we investigate the thermal conductivity of the latter nanostructures by means of classical non-equilibrium molecular dynamics simulations. Next, thermal conductance at the interface between a single wall carbon nanotube (nanofin) and water molecules is assessed by means of both steady-state and transient numerical experiments. Conclusions: Numerical evidences suggest a pretty favorable thermal boundary conductance (order of 107 W·m-2·K-1) which makes carbon nanotubes potential candidates for constructing nanofinned surface