פוסטרים TED

ד”ר רמי מסרי, המחלקה להנדסת מכונות

תחום המחקר: התפשטות חללים במוצקים והישום למכניקת חדירה ופריצה של מטרות מיגון

תקציר:

The worldwide research of ballistic penetration and perforation of metallic shields, for a variety of protection applications, is mostly governed by experimental and numerical studies, while analytical models are less available due to the extremely complicated nature of the subject. Sufficiently thick metal targets are perforated by rigid, sharp-nosed projectiles, in a mechanical process that is governed by a ductile hole enlargement mechanism. Several recent studies by the author have shown that the specific cavitation energy sc, which reflects the target material resistance to steady hole expansion, is essential for analytical predictions of ballistic limit velocities. The ballistic limit velocity Vb is the minimum impact speed that is required for a rigid projectile, with shank diameter D and mass M, to perforate a protective target, with thickness h and material resistance sc. A logarithmic formulation of the specific cavitation energy sc for metal targets, which is based on the concepts of (spherical cavitation) effective yield stress and hole slenderness ratio, is shown in several recent studies by the author, to be very useful for analytical predictions of ballistic limit velocities. The logarithmic formulation of sc is presented, and the concepts of cavitation effective yield stress and hole slenderness ratio are discussed. Based on the logarithmic formulation of sc, a new formula for the ballistic limit velocity Vb is presented and its excellent accuracy is demonstrated by a comparison to a very large experimental data base.

המחקר שיוצג שייך לתחום הכללי של פיתוח מודלים מתמטיים לבעיות פיזיקאליות ותיקופם בעזרת השוואה לניסויים. בפרט עוסק המחקר הנדון בפיתוח נוסחה מדויקת לחיזוי המהירות הבליסטית של מטרות מתכתיות המשמשות כמיגון בליסטי כנגד חודרנים קשיחים בעלי חרטום מחודד.

פרופ’ מרק ילין, המחלקה למתמטיקה שימושית 

תחום המחקר: Complex Dynamical Systems

שותפים למחקר: פרופ’ דוד שוחט וד”ר פיאנה יעקובזון

תקציר:

It is well known that local and global inverse function theotems play important role in analysis. Non-linear resolvents, in turn, are inverse mappings, while their existence follows by their definition and is not connected to the inverse function theory.
Recently, the existence of resolvents was used in [1] to obtain global distortion properties of inverse functions in a domain.
It turns out that these new properties of inverse functions can be used to describe various properties of resolvents, such as distortion and covering theorems, to establish orders of starlikeness and spirallikeness and so on, see [2].
Thus, we really show the mutual influence of classical analysis results and non-linear analysis.

ד”ר יריב מרמור, המחלקה להנדסת תעשייה וניהול

תחום המחקר: סטטיסטיקה: תפעול מערכות שירות

שותפים למחקר: Dr. Boris Shnits (Braude – College of Engineering, Karmiel), Dr. Illana Bendavid (Braude – College of Engineering, Karmiel)

תקציר:

It is safe to assume that classifying patients and generating multi-type distributionsof service duration, instead of using a general distribution for all patients, would yield abetter appointment schedule. One way to generate multi-type distributions is by using data mining. CART, for example, will generate the best tree, from a statistical perspective, nevertheless one could argue that most times, right from the base of the tree, the marginal contribution of each split decreases and at some point, for practical uses it is meaningless to continue further deep into the tree. Thus, from an operational perspective, the question arises – what is the benefit of using the whole tree compared to the much shorter (simpler) tree version? We explore and answer this question using an appointment case study. We start by comparing the operational measurements (i.e.,end of day, utilization, idle time and over time) using the whole tree for theappointment scheduling vs. applying the shorter tree versions. The results show that for all measurements there is a benefit in bigger trees until a certain point. After that, we can see some benefit, but it is not statistically significant nor meaningful. We further investigate how well the findings are robust under different daily patients mix. It seems that appointment scheduling based on bigger trees works better on average, but it doesnot have a relative advantage when patients’ mix results in loaded days.

ד”ר יריב מרמור, המחלקה להנדסת תעשייה וניהול

תחום המחקר: תכן ותפעול מערכות שירות

שותפים למחקר:  Dr. Yossi Luzon (Afeka, College of Engineering)

תקציר:

Modeling and data mining to construct anappointment book for surgery in a large hospital to reduce the time from call to surgery. The methodology has anoffline planning stage and a real-time online adjustment phase. We evaluate the algorithm on a real-world problem(about 1500 surgeries). Sensitivity analysis shows how the model parameters affect the performance of our model.

פרופ’ יניב אלמוג, המחלקה למתמטיקה שימושית

תחום המחקר: מתמטיקה שימושית ומשוואות דיפרנציאליות חלקיות

תקציר:

Theoretical population ecology uses mathematical models in order to understand the mechanisms which govern the dynamics of populations of organisms. Exploring how the dispersal of organisms interacts with environmental heterogeneity, both spatial and temporal, to determine population growth, is a central theme in ecological theory, with important implications for environmental management and conservation. Much work has been devoted to studying models of populations of a species inhabiting distinct areas (“patches”), coupled by dispersal among them.

Dispersal-induced growth (DIG) is a surprising phenomenon that has been identified by theoretical ecologists, and has also been experimentally verified. DIG occurs when several populations inhabiting distinct patches, with time-varying growth rates, each of which, when isolated, would become extinct, are able to persist and grow exponentially when dispersal among the patches is present. This work provides a mathematical exploration of this surprising phenomenon, in the context of a deterministic model with periodic variation of growth rates, and characterizes the factors which are important in generating the DIG effect, and the corresponding conditions on the parameters involved. It is shown that for the DIG

effect to occur, the frequency of the periodic environmental variations must be sufficiently small, and the rate of dispersal among patches must be neither too small nor too large. The mathematical results are based on the study of linear systems of differential equations with periodic coefficients (Floquet theory) and new results that have been obtained in this field in recent years.

פרופ”ח חגי כתריאל, המחלקה למתמטיקה שימושית

תחום המחקר: אקולוגיה מתמטית

תקציר:

Theoretical population ecology uses mathematical models in order to understand the mechanisms which govern the dynamics of populations of organisms. Exploring how the dispersal of organisms interacts with environmental heterogeneity, both spatial and temporal, to determine population growth, is a central theme in ecological theory, with important implications for environmental management and conservation. Much work has been devoted to studying models of populations of a species inhabiting distinct areas (“patches”), coupled by dispersal among them.

Dispersal-induced growth (DIG) is a surprising phenomenon that has been identified by theoretical ecologists, and has also been experimentally verified. DIG occurs when several populations inhabiting distinct patches, with time-varying growth rates, each of which, when isolated, would become extinct, are able to persist and grow exponentially when dispersal among the patches is present. This work provides a mathematical exploration of this surprising phenomenon, in the context of a deterministic model with periodic variation of growth rates, and characterizes the factors which are important in generating the DIG effect, and the corresponding conditions on the parameters involved. It is shown that for the DIG

effect to occur, the frequency of the periodic environmental variations must be sufficiently small, and the rate of dispersal among patches must be neither too small nor too large. The mathematical results are based on the study of linear systems of differential equations with periodic coefficients (Floquet theory) and new results that have been obtained in this field in recent years.

ד”ר בוריס שניץ, המחלקה להנדסת תעשייה וניהול

תחום המחקר: שיבוץ

תקציר: היום ארגונים בכלל ומערכות ייצור בפרט פועלים בסביבה מאוד תחרותית ודינאמית. זה דורש ממערכת ייצור יכולת לייצר מגוון מוצרים בכמויות קטנות, להסתגל מהר לשינויים בביקוש ובמוצרים המיוצרים, ולהגיב מהר לאירועים בלתי צפויים (כגון, הגעת הזמנות בלתי מתוכננות, נפילת מכונות ועוד).
על מנת להתמודד עם האתגרים הנ”ל המערכות צריכות להיות גמישות ויעילות. אחד ממערכי הייצור הגמישים ביותר הוא flexible job-shop. במערך זה ניתן לייצר מגוון מוצרים שונים כאשר לכל מוצר ניתוב הייצור (סדר פעילויות) משלו וקיימת אפשרות להשתמש במכונות אלטרנטיביות עבור הפעילויות. האפשרות להשתמש בניתובים/מכונות חלופיים/ות מקנה למערכת יכולת לאזן טוב יותר עומסים בין המכונות ולהתמודד בצורה טובה עם אירועים בלתי צפויים. אולם, מדובר במערך ייצור מורכב לניהול ולתפעול, ועל מנת לנצל את יתרונותיו ואת הגמישות שלו המערכת צריכה יכולת להסתגל בזמן אמת למצב עדכני של רצפת הייצור, כלומר לקבוע או לעדכן את שיבוץ העבודות למכונות בזמן אמת בתגובה לשינויים שקורים.
מחקר זה מתמקד בפיתוח מתודולוגיית שיבוץ דינמי עבור סביבת הייצור flexible job-shop שתוארה למעלה. הגישה המוצעת מבוססת על אופטימיזציה מקומית, כלומר פתרון בכל נקודת החלטה בעיית שיבוץ לוקאלי עבור המצב העדכני של רצפת הייצור. פתרון בעיות השיבוץ מתבצע באופן מתגלגל וכל פעם מתקבל שיבוץ מיטבי עדכני של עבודות למכונות עבור תקופת השיבוץ הקרובה. גישה זו מאפשרת הן לקבל שיבוצים מיטביים ומותאמים למצב רצפת הייצור עבור תקופת הזמן הקרובה והן לפתור את בעיות השיבוץ בזמן סביר.
המתודולוגיה שפותחה נבחנה על ידי השוואת ביצועיה לביצועים של גישות שיבוץ דינמי ידועות. התוצאות מראות שהמתודולוגיה המוצעת מביאה מערכת ייצור לביצועים טובים יותר במדדים המרכזיים שנבחנו ומאפשרת לנצל טוב יותר את הפוטנציאל של flexible job-shop.

הידעת?
ד”ר בוריס שניץ הוא מרצה בכיר במחלקה להנדסת תעשיה וניהול. הוא חוקר ומלמד קורסים בתחומים של תכן ותפעול מערכות ייצור ושירות ומערכות ייצור משולבות מחשב.

פרופ”ח אמיל בשקנסקי, המחלקה להנדסת תעשייה וניהול

תחום המחקר: הנדסת איכות, מדע נתונים

שותפים למחקר: ד”ר יריב מרמור

תקציר:

The partitioning of the data into clusters, carried out by the researcher in accordance with a certain criterion, is a necessary step in the study of a particular phenomenon. Subsequent research should confirm or refute the appropriateness of such a division, and in a positive case, evaluate the discriminating power of the criterion (or, in other words, the influencing power of the factor according to the level of which the data was divided). If the data comes from a metric space, this means that for any pair of data, a distance is defined that characterizes the dissimilarity between them. Speaking of data, we are not necessarily talking about numbers, it can be information of any kind about the objects under study (such as spectrograms, 3B forms, etc.) obtained as a result of measurement, observation, query, etc., however distance between data, expressing how far apart the objects of interest are represented by a scalar. The correct choice of the distance metric is a fundamental problem in quality control, pattern recognition, machine learning, cluster analysis, etc. We propose two universal discriminating statistics – SP (segregation power) based on the ratio and the difference of inter to intra clusters’ correlated estimates of the distance between objects and discuss their specificity and sensitivity as well as their universalism and robustness in relation to the type of objects under study.

ד”ר אופיר שנבל, המחלקה למתמטיקה שימושית

תחום המחקר: מתמטיקה- אלגברה אבסטרקטית

שותפים למחקר: Leo Margolis

תקציר: 

In projective representation theory the role played by twisted group rings of a group G over a commutative ring R is in many ways similar to the role of the group ring RG in the representation theory of G over R.
The classical group ring isomorphism problem (GRIP) is to determine which information about G is encoded in the group ring RG. Similarly, the twisted group ring isomorphism problem (TGRIP) is to determine which information about G is encoded in all the twisted group rings of G over R. While GRIP was presented nearly 80 years ago, TGRIP was introduced in 2016 by L. Margolis and O. Schnabel.
In 3 papers we study TGRIP over fields. A key notion here is to construct tools to study TGRIP that will play a similar role to the classical tools used in the study of GRIP. Two particular cases are 1) the study of commutative simple components of twisted group rings, and 2) constructing a generalized Schur cover of a group when the field is not algebraically closed.
Other motivations we explore:
1. The differences between TGRIP and GRIP.
2.The differences between TGRIP over the complex numbers and TGRIP over other fields.

In both, we present significant results in our papers.
Some of our goals for the future are:

1. To prove the twisted Brauer’s problem or to find a counterexample.
2. To investigate TGRIP for p-groups over fields of characteristic p (i.e. the modular case).

פרופ”ח אהוד קרול, המחלקה להנדסת מכונות

תחום המחקר: תכן

שותפים למחקר:  Lauri Koskela, University of Huddersfield

תקציר: 

Design process descriptions in the literature in general and those using C-K theory in particular lack some useful cognitive information that may affect the credibility of the process. Notions from abduction research are presented and proposed for enhancing such descriptions. Specifically, it is important to distinguish between design activities that are intuitive and those that result from deliberation; a topic that has long been discussed by philosophers of science and design scholars. The focus of the paper is on the ubiquitous design moves of proposing an idea and selecting among ideas, and on their execution by expert and novice designers.

פרופ”ח אביב גיבלי, המחלקה למתמטיקה שימושית 

תחום המחקר: מודלים ושיטות איטרטיביות במתמטיקה שימושית

שותפים למחקר: Francisco J. Aragón Artacho, Yair Censor, Karl-Heinz Küfer

תקציר: 

Optimization models consist of decision variables, an objective (cost) function that needs to be maximized/minimized and some constraints. In some real-world applications such as radiotherapy, the goal is to find a treatment that fulfils all constraints, i.e., no objective function is involved. Such problems are called feasibility problems.

In other applications, for example, in image reconstruction, the goal is to recover an image from some noisy measurements. In various scenarios like in medical imaging, it’s not sufficient to find a feasible solution and thus an additional objective is introduced that captures the desired recovered image structure.

In this talk I will present several applications that are modelled either as feasibility oroptimization models and methods for solving them, mainly projection methods and superiorization.

ד”ר  אליעזר חנוכה, המחלקה להנדסת מכונות

תחום המחקר: 

שותפים למחקר:

תקציר: 

Nonlinear Finite Element Method is the most widely used numerical technique to solve engineering problems associated with nonlinear solid continua. To apply this numerical technique, numerical integration is required for the element-level computations. Most commonly, a standard quadrature method (e.g., Gauss points) is employed. Consequently, computational complexity increases linearly with the number of integration points. Therefore, the derivation of alternative integration approaches to reduce computational resources is beneficial.

Herein, we propose new Semi-Analytical element-level integrators. Our formulae identically admit the “full integration” requirement for the nonlinear formulation. The suggested schemes can be viewed as case-specific integrators i.e., unique integration formula to evaluate the internal forces, mass, and the nonlinear stiffness matrix. Computationally, Semi-Analytical integration rules are roughly equivalent to one-point quadrature.

To this end, the integrands are reformulated (decomposed) into two multiplicative parts. The first part includes kinetic and kinematic functions which admit “full integration” criteria for one sampling point (e.g., the centroid). While the second part consists of mesh and displacement-independent polynomial functions. We integrate the above polynomials analytically, to derive coefficient sets. Those coefficients are incorporated in the integration subroutine. Overall, code implementation requires a one-time pre-computation of the coefficient according to the supplied formula.

The research has been conducted at the Braude College of Engineering. Its potential application includes adoption of the suggested formulae by the commercial and scientific software FE simulation packages