Isolating vacuum amplitudes in quantum field calculations at finite temperature

In calculating Feynman diagrams at finite temperature, it is sometimes convenient to isolate subdiagrams which do not depend explicitly on the temperature. We show that, in the imaginary time formalism, such a separation can be achieved easily by exploiting a simple method, due to M. Gaudin, to perform the sum over the Matsubara frequencies. In order to manipulate freely contributions which may be individually singular, a regularization has to be introduced. We show that, in some cases, it is possible to choose this regularization in such a way that the isolated subdiagrams can be identified with analytical continuations of vacuum n-point functions. As an aside illustration of Gaudin's method, we use it to prove the main part of a recent conjecture concerning the relation which exists in the imaginary time formalism between the expressions of a Feynman diagram at zero and finite temperature.Comment: 37 pages, 12 figure

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The thermal operator representation for Matsubara sums

We prove in full generality the thermal operator representation for Matsubara sums in a relativistic field theory of scalar and fermionic particles. It states that the full result of performing the Matsubara sum associated to any given Feynman graph, in the imaginary-time formalism of finite-temperature field theory, can be directly obtained from its corresponding zero-temperature energy integral, by means of a simple linear operator, which is independent of the external Euclidean energies and whose form depends solely on the topology of the graph.Comment: 9 pages, 1 figure, RevTe

Di-μ2-bromido-bis­[bromido(η6-1,2,4,5-tetra­methyl­benzene)ruthenium(II)]

The asymmetric unit of the title compound, [Ru2Br4(C10H14)2], contains one half of the centrosymmetric mol­ecule. Each Ru center is coordinated by tetra­methyl­benzene ring in a η6-coordination mode, and one terminal and two bridging bromine atoms. The aromatic rings and the Ru2Br2 four-membered ring form a dihedral angle of 55.99 (8)°. In the crystal structure, weak inter­molecular C—H⋯Br inter­actions link mol­ecules into chains propagated in [001]

Di-μ2-chlorido-bis­[chlorido(η6-hexa­methyl­benzene)ruthenium(II)]

Dimeric mol­ecules of the title compound, [Ru2Cl4(C12H18)2], are located on a crystallographic centre of inversion with one mol­ecule in the asymmetric unit. The hexa­methyl­benzene rings are in an η6-coordination to the ruthenium centres, which are bridged by two chloride ligands. In addition, the ruthenium centres are bonded to another chloride ligand. The aromatic rings and the Ru2Cl2 four-membered ring enclose a dihedral angle of 55.85 (6)°

Damages and matter ejection during HVI on brittle structures: implications for space environment

The population of space debris is suspected to grow on earth’s orbits. This might be due to self generation processes occurring when an object impacts a satellite’s surface. As brittle materials, widely used for large solar arrays, are particularly sensitive to HVI in terms of damage and matter ejection, they might play an important role in debris generation. This paper focuses on HVI on thin brittle targets like Hubble silicon solar cells. Simulated and in-situ Front back impacts on both HST-CS and simple SiO2 targets were analyzed. Ejected volume and fragments were collected and filmed to characterize potential secondary debris. A mechanical analysis of damages due to the multilayered structure of solar cells as well as Ls-Dyna SPH calculations have also been performed and are compared to experimental results to assess predictions capabilities of the SPH code

Modelling kinematics and cutting forces in vibration assisted drilling

One of the main drawbacks of the traditional drilling process is the formation of long chips when cutting metallic parts. Usually, peck drilling cycles are used to break and evacuate the chips through the flutes of the drill. However, this solution increases the operation time and therefore decreases the productivity. To solve this problem, vibration assisted drilling has been developed to meet industrial needs in terms of productivity. Forced vibrations impose a variation of the chip thickness in order to obtain its fragmentation. This process has been recently developed and optimal cutting conditions have yet to be determined to improve it furthermore. This paper presents, on the first hand, an experimental study of the kinematics of vibration assisted drilling. It showed a strong reduction of the amplitude of vibration during drilling, in the configuration of the tests. In addition, tests were conducted to show the apparition of interference phenomena at the centre of the tool. Interferences are difficult to separate from the cutting phenomenon, making the modelling of cutting forces difficult. From the kinematic model, chip height can be simulated in order to model the cutting forces. A thrust force and a torque model applied to vibration assisted drilling are presented in this paper. The thrust force model is based on a representation of the tool by several zones corresponding to each cutting mechanism: indentation at the centre of the tool, cutting along the cutting edges and bad cutting conditions in an intermediary zone. The periodically variable feed speed modifies the size of each zone and the thrust force they generate. The model presented in this paper formulates the interaction of several zones of the tool with the material and explains the particular shape of the thrust force observed. The models are identified and validated through an application on aluminium alloy 7010

Biomineral repair of Abalone shell apertures

The shell of the gastropod mollusc, abalone, is comprised of nacre with an outer prismatic layer that is composed of either calcite or aragonite or both, depending on the species. A striking characteristic of the abalone shell is the row of apertures along the dorsal margin. As the organism and shell grow, new apertures are formed and the preceding ones are filled in. Detailed investigations, using electron backscatter diffraction, of the infill in three species of abalone: Haliotis asinina, Haliotis gigantea and Haliotis rufescens reveals that, like the shell, the infill is composed mainly of nacre with an outer prismatic layer. The infill prismatic layer has identical mineralogy as the original shell prismatic layer. In H. asinina and H. gigantea, the prismatic layer of the shell and infill are made of aragonite while in H. rufescens both are composed of calcite. Abalone builds the infill material with the same high level of biological control, replicating the structure, mineralogy and crystallographic orientation as for the shell. The infill of abalone apertures presents us with insight into what is, effectively, shell repair

Plant height and hydraulic vulnerability to drought and cold

Understanding how plants survive drought and cold is increasingly important as plants worldwide experience dieback with drought in moist places and grow taller with warming in cold ones. Crucial in plant climate adaptation are the diameters of water-transporting conduits. Sampling 537 species across climate zones dominated by angiosperms, we find that plant size is unambiguously the main driver of conduit diameter variation. And because taller plants have wider conduits, and wider conduits within species are more vulnerable to conduction-blocking embolisms, taller conspecifics should be more vulnerable than shorter ones, a prediction we confirm with a plantation experiment. As a result, maximum plant size should be short under drought and cold, which cause embolism, or increase if these pressures relax. That conduit diameter and embolism vulnerability are inseparably related to plant size helps explain why factors that interact with conduit diameter, such as drought or warming, are altering plant heights worldwide