Operational modal analysis with non stationnary inputs

Operational modal analysis (OMA) techniques enable the use of in-situ and uncontrolled vibrations to be used to lead modal analysis of structures. In reality operational vibrations are a combination of numerous excitations sources that are much more complex than a random white noise or a harmonic. Numerous OMA techniques exist like SSI, NExT, FDD and BSS. All these methods are based on the fundamental hypothesis that the input or force applied to the structure to be analyzed is a stationary white noise. For some applications this hypothesis is reasonable. However in numerous situations, the analyzed structure is subject to harmonic and transient forces. Numerous methods and research has enabled to develop methods that are robust to such harmonic contributions. To enable OMA during pressure oscillations in solid rocket boosters, the authors propose to consider transient and harmonic inputs no longer as parasites but as the main force applied to the structure that must be analyzed. This is the case during pressure oscillations in rocket boosters. We propose the use of phase analysis adapted to a transient context to conduct operational modal analysis under a harmonic transient input. This time-based novel OMA method will be exposed. The theoretical developments and algorithmic implementations are exposed. First tests have been conducted on laboratory single degree of freedom setup to validate this new OMA technique and are reported here

Scale-down emulsion homogenization: Conditions to mimic pilot homogenizer depending on the emulsifier

The standard tool for emulsification during formulation trials is a homogenizer, which unfortunately requires toomuch raw material and is time consuming. A lab-scale process using a rotor-stator shearing step followed byultrasound treatment was designed, both with lecithin and whey protein, for emulsification as efficient as inpilot-plant trials. Ranges for the lab-scale process were defined (rotor-stator: 5 min, 5000–10000 rpm; sonicationtime: 2–10 min). Process conditions were identified to obtain both emulsions with the same structure at lab andpilot scales: for lecithin, respectively shearing at 10000 rpm/10 min sonication and high pressure for both pilotstages. However, due to protein denaturation, some conditions differed for whey proteins: shearing at 5000 rpminstead of 10000 rpm (all the other parameters being unchanged). Finally, recommendations concerning theposition of the ultrasound probe and temperature control are provided to insure good reproducibility

Confocal microscopy of bread dough under controlled thermo-mechanical treatment

International audienceThe rheology of bread dough is known to be complicated. However, it was extensively studied using both empirical and fundamental rheology characterizations. Many studies proposed correlations between rheological properties and macroscopic behavior such as elastic recovery after shaping or alveolar structure after proofing and cooking. The protein gluten network is recognizing to play a major role on the rheology of the dough. On the other hand, dough microstructure was observed at different scales using microscopy techniques such as CSLM. However, to our knowledge, no study exists on the direct observation of the evolution of the gluten organization at microscopic scale under shearing and heating. Using a home made rheo-optic device mounting on a confocal microscope, bread dough for different composition (water, sugar and oil contents) under continuous or oscillating strain was studied to find the optical signature of microstructure changes in relation with shear-thickening effect previously measured. This device allows controlling the strain and the shear rate but also the temperature of the dough, all parameters causing changes in gluten microstructure. It was shown that the higher the water content or the sugar content, the stiffer was the gluten strands but the less continuous the network before shearing and the more reinforced were the gluten strands under shearing. Moreover, the oil could be observed in the form of droplets located at the dough/bubble interface and in the form of gluten/oil co-localisation areas around the bubbles. Shearing the dough using an oscillatory strain signal leaded to an increase of the co-localisation areas. Finally, by a controlled increase of temperature, the growth of an air bubble in bread dough containing yeast was followed during proofing. The influence and the disposition of fat globules at the bubble air-protein interface along this growing process were followed

On Maximal QROBDD's of Boolean Functions

We investigate the structure of ``worst-case'' quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of ``hard'' Boolean functions as functions whose QROBDD are ``worst-case'' ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer)

Mahler's expansion and boolean functions

International audienceThe substitution of X by X2 in binomial polynomials generates sequences of integers by Mahler's expansion. We give some properties of these integers and a combinatorial interpretation with covers by projection. We also give applications to the classification of boolean functions. This sequence arose from our previous research on classification and complexity of Binary Decision Diagrams (BDD) associated with boolean functions

HFE and BDDs: A Practical Attempt at Cryptanalysis

HFE (Hidden Field Equations) is a public key cryptosystem using univariate polynomials over finite fields. It was proposed by J. Patarin in 1996. Well chosen parameters during the construction produce a system of quadratic multivariate polynomials over GF(2) as the public key. An enclosed trapdoor is used to decrypt messages. We propose a ciphertext-only attack which mainly consists in satisfying a boolean formula. Our algorithm is based on BDDs (Binary Decision Diagrams), introduced by Bryant in 1986, which allow to represent and manipulate, possibly efficiently, boolean functions. This paper is devoted to some experimental results we obtained while trying to solve the Patarin's challenge. This approach was not successful, nevertheless it provided some interesting information about the security of HFE cryptosystem

On Maximal QROBDD's of Boolean Functions

We investigate the structure of ``worst-case'' quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of ``hard'' Boolean functions as functions whose QROBDD are ``worst-case'' ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer)

On maximal QROBDD's of Boolean functions

We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer)

HFE and BDDs: A Practical Attempt at Cryptanalysis

HFE (Hidden Field Equations) is a public key cryptosystem using univariate polynomials over finite fields. It was proposed by J. Patarin in 1996. Well chosen parameters during the construction produce a system of quadratic multivariate polynomials over GF(2) as the public key. An enclosed trapdoor is used to decrypt messages. We propose a ciphertext-only attack which mainly consists in satisfying a boolean formula. Our algorithm is based on BDDs (Binary Decision Diagrams), introduced by Bryant in 1986, which allow to represent and manipulate, possibly efficiently, boolean functions. This paper is devoted to some experimental results we obtained while trying to solve the Patarin's challenge. This approach was not successful, nevertheless it provided some interesting information about the security of HFE cryptosystem

Mahler's expansion and boolean functions

International audienceThe substitution of X by X2 in binomial polynomials generates sequences of integers by Mahler's expansion. We give some properties of these integers and a combinatorial interpretation with covers by projection. We also give applications to the classification of boolean functions. This sequence arose from our previous research on classification and complexity of Binary Decision Diagrams (BDD) associated with boolean functions